One of the most interesting fields to ponder on in regards to this type of question is biological anthropology. Two very similar relatives of ours are bonobos and chimps. 97%-99% of the genetic base pairs are shared, so a bit counter-intuitively, the average human male has more common base pairs with a male bonobo than with a female human.
Now for the weird part. Regular chimps are like real-world humans: male-dominated societies, lots of violence, etc. Their near-identical twins, the bonobos, are matriarchal. Even though males are still larger, females are still the ones who get pregnant, basic evolutionary game theoretic incentives are the same etc., one species is patriarchal, one is matriarchal. Weaker bonobo females band up against violent males and kick them out of the group. It's really, really weird.
Makes you wonder, doesn't it? How would human societies have evolved had we been just a little bit more bonobo-like than chimp-like? Perhaps human 'herstory' would consist of a 20,000 year peace?