Our closest genetic relative actually has a female dominated society, so there is a great example in them for why females would dominate. However, before we get into them let's get some context by first looking at the current common suggestion of using sexual dimorphism as a justification.
As a quick caveat I'm going to be talking allot about the evolutionary ancestors of your theoretical humanoid race, since their evolutionary ancestory is what will decide their instincts. The 'modern' version of this species may have a culture that encourages them to behave differently, in fact it likely will, but evolution of instincts happens before culture has really evolved.
Other's like big women but I cannot lie, this brother has to deny
...I think I tried way to hard to fit those song lyrics into a title topic...
The common suggestion seems to be to have females be larger then males, giving them dominance by physical size. It's true that there are many species that have sexual dimophism, but I don't think a humanoid species is likely to have dimophism favor larger women.
For the majority of species, and in particular the vast majority of mammals, sexual dimophism favors larger males, not larger females. Males traditionally have to compete with each other to earn the ability to mate with women. These competitions usually favor physical size and strength, and thus drive males to develop a larger size to make them better able to beat other males and achieve mating success. Females don't have this sort of evolutionary arm's race with other's of there species driving them to grow as large.
Meanwhile in females which care for their young (K select species) the female needs to consider not just size but caloric efficiency. Since a female needs to provide for her young she is going to be in a situation where she needs to collect enough food to provide for herself and her child, which is obviously harder then collecting enough food for yourself alone. Having a smaller body means she doesn't have to waste as much energy in maintaining it, which means she needs to eat less and thus can afford to provide more of her food to her children to allow them to grow faster.
Thus in general with mammals in particular you usually see males being larger, having spent all the 'extra' calories they can collect because they only have to care for themselves on bulking up so they can beat other males in mating challenges, and females being smaller and more efficient builds.
It's true that this isn't always the case, but for mammals it is very often true.
Bigger is only sometimes better
There are number of situations which can encourage larger females to males, most of them though involve mating strategies different then human, or most mammals, maintain. A list of some of these are:
- Males do the heavy lifting with caring for children.
Look at the seahorse as an example of this. The seahorse male put more caloric effort into caring for the children then the female does (though in sea horses it's close with female putting a decent amount of energy into creating the eggs). For this reason the female compete for the males and thus the females are the one encouraged to grow larger as part of competing for males.
This offers one means for a humanoid species to have females dominant. If female gave birth then gave the child over to the male and abandoned them, so the male put in all the effort of raising the child, this would make the male the coveted sex and females would have to compete for males leading to females potentially growing larger. However, this doesn't seem likely to evolve due to the length of a pregnancy and the difficulty of males being confident of the paternity of the female's child; which leads to little encouragement for males to play sole support for the child after birth, so I wouldn't recommend using this justification.
- R select species
With R select species (ones that have little young and provide no benefit for the young after birth) there is more incentive for the female to be larger, as larger size can make it easier to produce more eggs and thus more children per mating. This alone doesn't guarantee, by any means, that a female will be larger, but the vast majority of species that have a larger female are heavily R select species.
- polyandrous mating systems
When female will mate with many males, and generally mates with any males as they show up, competition between males is less common (since the female will mate both of them anyways why fight?), thus there is no longer factors pushing males to be larger.
None of these cases apply to a humanoid species, and as such the most common motivating factors for larger females won't apply. It's thus likely that males will be larger then females unless you significantly change the species in some way, such as by having females impregnate males a la seahorse scenario.
..let me say I've still simplified this by not bringing up a dozen other lesser examples that can drive evolution towards larger females, but still most of them likewise apply to non-mammal & heavy R select species and so won't apply to humanoids.
Males may still throw like a girl
I said that it's unlikely that females will be larger, but it's quite possible that males and females will be approximately the same size, or close to it. for instance if the early hominid was heavily monogamous then mate selection would likely be less based off of physical competition between males and males would thus likely be closer to female in size.
Alternatively a highly social humanoid species, where mating rights were achieved by social interaction and 'politics' more then physical brawn may lead to a species with lower sexual dimorphism.
In either case if females are dominant the mating strategies of these humanoids would likely be change to one that is less based off of male physical competition. I suspect a female dominated humanoid species would likely have very little sexual dimophism, with males and females both being approximately the same size.
Numbers beat brawn
So if females don't have a size advantage how can they dominate? One likely answer is by outnumbering the males. If males are at a numeric disadvantage in any competition, and there isn't a size advantage to help the males out, then the females are in the position of power.
The naive answer would be to say that more females are born then males so they always outnumber males. I've heard this suggested as a more 'efficient' mating strategy since there are more females able to produce young for the next generation. However, this is unlikely to happen. Fisher's principle should ensure that there are roughly the same number of males to females by the time they reach sexual maturity.
Still there are other ways to help ensure that women have the numeric advantage.
Don't bother saving up for retirement age
You will notice I only said that Fisher's principle generally ensures the same number of males at the point of sexual maturity. That doesn't mean that females can't end up outnumbering males. if males were to die early then the longer lasting females would still outnumber males.
Females already outlive males in modern society, but lets take it to a greater extreme. Maybe males are so busy competing for mating rights that they often die young in the competition, such that any given male only tends to see a few mating seasons before he likely dies. Since successful males would likely manage to mate with numerous females a male may be every bit as successful as a female at producing children (on average) despite not living nearly as long. In fact many species have males who die young due to this strategy.
If you were to go this route then the longer living females would ultimately outlive the males to such a degree that they would end up with numbers on their side, think to the numerous older females who outlive their male counterparts. Thus the females would have the numeric superiority to allow them to dominate the females.
This strategy would likely work, but it would result in a rather different humanoid species. Males would likely not be quite as smart as females. In a modern society males will likely survive much longer then the few seasons their primitive counterparts got, but their life would likely still be relatively short, and they may not be encouraged to attain higher level education since they would die of old age before they had time to work for long in whatever field they spent more then half their life mastering. The males would likely also be encouraged to do any dangerous jobs, like being soldiers, since they have such a short life expectancy anyways.
I heard your herd likes to hoard all the power
An easier solution is to have female in a larger herd that outnumber any grouping of males they currently are in contact with . Already with most herd species one sex will usually be driven out at sexual maturity (to avoid inbreeding), so imagine for your humanoid species the males are driven away. The females all stick together as a family unit making a larger herd, while the males make smaller groupings of males.
Of course you need to make sure that the males don't just develop one large herd of their own, where they have similar numbers to females if you want females to outnumber them. I'd suggest if you went with this scenario having the males only group with genetically related males. So for instance every season when a female herd drives out their males all the males from that herd group together to make a single small bachelor pod. Since all the females in the original herd were likely related (as daughters and granddaughters of the original matriarchs stuck around) this would mean all the males driven from the herd likely have some degree of genetic relatedness.
The males all being close genetically would give them an evolutionary incentive to grouping up and work together to protect each other. By helping to protect their half-brother's in the bachelor pod the males gain an indirect evolutionary fitness by increasing the fitness of their half-brother in hopes that half-brother will successfully mate and pass on some of the other males genetics. This would result in a number of smaller male bachelor pods that band together, but don't necessarily want to cooperate with other, unrelated, males groups. Thus ensuring a female herd, with multiple generations of females living together, will usually be noticeably larger then any male bachelor pod.
Thus the female herds will have the numbers to out-compete male bachelor pods whenever they encounter each other, putting females in a dominate position. For males to develop an instinctual submissiveness to females your likely want males to encounter females more often then just during mating season. If you have females often encountering the male bachelor pods when, for instance, foraging then you have a good situation for encouraging a natural dominance/submission interaction. Whenever a bachelor pod runs into a female herd it would need to know to be submissive and give the females first choice of foraging rights, since they need to avoid a fight that the female's larger herd would ensure females would win. Constant interactions over food over generations would translate this principle to an instinctual tendency for males to back down in conflict with females.
If you went this route I would suggest that you have females and males having lots of interaction to help further social development and skills, which are a key driver of intellect, and to ensure both sexes develop altruism and social cooperation skills required for modern humanoids to work together in an inter-sex social enviroment. I'd suggest males claim a territory with females wondering, with the larger female territory encompassing a few male territories. While females are in one bachelor pod's territory the males join with and intermingle with the female herd, interacting socially, trading favors, and generally with males trying to encourage females to choose the male to mate with. This isn't required, but it seems to help drive the sort of society your more likely to want for your modern humanoids.
Of course there is an even easier approach that takes elements of this approach but doesn't require separate male bachelor pads, which makes it easier to justify humanoids developing social instincts like that of modern humans. It even has the benefit of being proven to work in nature...
Hippy Apes to the rescue
Thus we get to a working example of dominate females in the bonobos. If your not familiar with them the bonobo's are one of our two closest genetic relatives, being as close to us as the more commonly known chimpanzee. They are also a fascinating species, evolutionary speaking, having a number of traits that are rather unique for greater apes. They share our more upright walking posture and forward facing hips (their also the only other ape to mate 'missionary style' due to this). They are also by far the most peaceful ape species, usually resolving conflict without violence and studies show a more instinctual altruistic behavior then humans. And of course, women dominate their society.
I mentioned already that closely related apes benefit from grouping together to work together, and that bond of kinship is an important part of how the female dominated society developed in the bonobo. Males are driven out when they reach sexual maturity, just like I suggested in my last example, meaning that bonobo herds consist of genetically related females and unrelated males that migrated into their troop. This, in turn, means that the females have a larger incentive to band together then the males, since the females are far more inclined to help their sisters and daughters then the males are to help an unrelated male.
Thus while bonobo herds tend to have roughly the same number of males to females the females ended up in charge by developing an alliance together to allow the family of females to control the unrelated males in their troop. If a particular male attempts to cause trouble for any one female he will find multiple females ready to defend their sister/daughter/mother, but if a female tries to bully a male there is little reason for other unrelated males to come to his aid. Thus the inclination to side with your genetic relatives has proved the basis of the unspoken alliance that ultimately put bonobo women in charge.
Now I need to stop for a second to get into the reason why the bonobo's are called the 'hippy ape', since it impacts how the female alliance grew so powerful. Keep in mind your humanoids don't need to have the same strategy, but I need to discuss how it impacted bonobo evolution. Bonobo are accused of being hippies do to their strong belief in the old saying "Make love not war" They use sex as a form of conflict resolution, using it to resolve conflicts without violence, exchange favors, develop alliances, make up after a fight etc. They also have sex in every form you can imagine, with any combination of age and sex, you can't exclude anyone from a major part of your social conflict resolution system after all.
This benefited the females in two manners. First, it gave bonobo a means of ending a conflict without violence before female alliances were as strong, specifically by offering sex to a male to appease him. Females still do this often, by offering sexual contact (not always full matings) to help lower tension and resolve a conflict before it escalate to violence. Since males are far more driven to achieve matings then females (since females can only conceive once a year, whereas every mating a male has could theoretically result in a child), males were willing to end conflict or surrender resources to female in exchange for an opportunity to mate, giving women a clear source of power over the males since they had a monopoly on a 'resource' they could offer to males (an opportunity to mate), that they could trade for resources or social power.
The other benefit, less obvious but potentially as important, was obscuring who the father of a child was, since the female has mated with multiple males. This leads to males being unable to group together to form a counter group of related males to resist female dominance since no males knew how closely related they were to other males.
If your fine with your humanoid species utilizing a similar sex for conflict resolution and social interaction approach then you can copy the bonobo exactly as they are, up their intellect a bit while maintaining their social conventions, and have a nearly perfect example of what a female dominated humanoid species would be like.
If you don't want such an emphasis on sexual interaction in your humanoid species there are some options. First is to copy the bonobo, but claim that the degree of sexual contact decreased later in their evolution. A good explanation for this would be to claim as the bonobo society grew larger and more compact the risk of such an regular and intimate form of social contact spreading STIs would become very real, and it's possible the bonobo would have to have moved to less sexual forms of social bonding as death's via STIs grew to put a large evolutionary pressure on them. Thus you could create a modern bonobo and replace actual sex with some other form of social bonding activity potentially; though I suspect even if the bonobo had to move away from full intercourse due to STIs their bonding rituals would still be somewhat sexual in nature, such as brushing one's hand over anther's genitals as a calming action.
Alternatively you can try to create an ape species that likewise formed a female alliance based off of familiar bonds but never used the bonobo's approach.
what women want
I originally started writing a whole long explanation for why most apes still were male dominated, but it doesn't add much to the answer. It comes down to females needing to be the start ally together as the start of the original evolution from single individuals living independently to a more herd like living arrangement; but ultimately it boils down to "evolution just needs to go that way". there are a few ways it can go, and frankly you probably don't need to think too deeply about the evolutionary psychology.
Still there are a few things we can predict about a species that went down this evolutionary path.
- Males and females are approximately the same size.
this is required to ensure males don't have a size advantage that makes it easier to dominate women before they have started to ally together
- They likely had a polyandry lifestyle.
Women likely mated with many men, likely to hide mate choice as human females did. This both helps to ensure little sexual dimorphism (since males have less need to fight for mating rights there is little advantage in males growing larger), and helps to hide paternity of a child to prevent males from knowing how related they are or developing a similar alliance based off of genetic closeness. Your modern humanoids may now have a more monogamous lifestyle, humans did transition towards a culturally inspired monogamous one after all.
- social maneuvering is king.
With physical power being less relevant to males earning mating rights the emphasis would have moved towards having better social skills, convincing females they should want you as a mate. This would mean the species may be less prone to physical aggression, but that the species is also more prone to politics, social maneuvering (including stabbing others in the back), and all the other potential headaches of a species that emphasis social status above everything else would be willing to resort to to keep that status.
- It's all about who your mother is.
This society is driven by familiar bonds. Females rose to power due to willingness to ally with those who shared genetics with them to gain power over those that didn't. Their very instinct will more strongly emphasis the concept of supporting your family at all costs, even more then humans. This means tracing family lineage, inheriting influence/power based off of your family, and wars between influential families will all be more common then in humans. Though your maternal family line is what will matter, your paternal family likely gets far less influence or meaning in their culture.