I think it's important to bear in mind that evolution is incidental; the initial existence of a particular trait (advantageous or otherwise) is a matter of chance mutation.
So the reason we find a particular species to be hermaphroditic might not be because hermaphroditism itself formed the foundation for them to grow into their most recent niche. It might be because the first mutations which enabled some particular progenitor species to inhabit that niche simply occurred, incidentally, in a hermaphrodite. Contrariwise, it may be that sex distiction only developed in species occupying another niche entirely than the one to which the forebearer species of note in this exercise were acclimating themselves. If the alternative doesn't even come up, is there really an "advantage" to talk about?
We may also bear in mind that existing traits only become more or less prominent under selective pressure, which may or may not be ongoing at any given time in an evolutionary history.
So the last time that your nature as a hermaphrodite was highly relevant or that there was a chance that sexual distinction might have teniably developed in an ancestor of yours may have been very, very far back in your evolutionary history.
For example, hermaphrodites fair better at initial colonization and sustaining through near-extinction events than sexually distinct reproducers do, because they have less difficulty finding mates in sparse populations and every specimen can be a breeding mother. Imagine if you had a primordial ocean, full of creatures both sexed and hermaphroditic, but the dry land is unoccupied and inhospitable. If the first creatures with a preponderance to land-dwelling have sexes, and shortly after they establish themselves on land there's an environmental calamity that drives down their numbers significantly, they have a much greater chance of being left with too few breeding mothers, obsticles separating many of the viable breeders of either gender, or a pedigree collapse. Hermaphrodites are much more interchangable and can deal better with these problems. Also, if an individual specimen is carried far from its group, then it needs to be an impregnated female for it to have a hope of establishing a new colony alone (if indeed it's even a creature that has internal pregnancy). Hermaphrodites, on the other hand, can usually self-impregnate and struggle through as long as there's just one viable breeder at any given time.
But for those creature's well-established descendents 400 million years later, it could be that none of that matters anymore! Certainly, for you and me these aren't very big issues.
I suppose I could think of other times in evolutionary history where these things come up, but I'm not certain this is what you're looking for; I suspect that you're interested in writing a well-developed sentient hermaphroditic species of a more-or-less modern character. But if I'm being tangential in any way, may I interest you in alternative condolidated-gender lifestyles?
We know of many kinds of fish that develop into a different sex in different stages of life. So, you can have a model where young creatures are female (for maximum number of brood mothers) and the older creatures are male (for maximum selectivity). Or you could do it the other way around, I suppose, so that the young adventurous ones go and find a new tribe to breed with, and in being smaller only need to make the tiny gametes, and the old ones are tired and sedentary or are are just big enough to deal with pregnancy or laying big eggs.
Angler fish do this thing where young males go bite a female and then merge with her body, wasting away into just a set of genitals. This isn't truly hermaphroditic but it does result in individuals who are inately female but still bristle with penises.
Ants and bees are female if they hatch from a fertilized egg, but otherwise male. So maybe you've got a society where everyone who matters is a lady but rather than fuck each other personally, they just occasionally give birth to a bunch of tiny idiot expendable sons and throw those guys in each other's faces. To me, it just sounds like making sperm with some extra steps.
Genetic recombination is crazy, and raises the question: is your cell division really asexual if you're getting your genetic material all up in each other's business during your downtime? Imagine a world where everyone appears to be breeding asexually, though on closer examination they're actually totally infested with a sympathetic virus that only proliferates in their genital tissues but which is highly communicable and carries full copies of their genome. Then they're impregnating each other all the time with vast repertoires of genetic information and probably have some significantly weird diseases that I don't even care to anticipate and this is probably ridiculous but it's yours if you want it I guess.