Men are naturally better~From Human: The Science Behind What Makes Us Unique by Michael S. Gazzaniga, page 69:
Wrangham [professor of biological anthropology at Harvard] reports that observational studies have found chimps to be patriarchal. Males are dominant, inherent territory, raid and kill their neighbors, and gain the spoils (not only increased foraging, but neighboring females), but they also are killed if they lose their territory. Females, however, gain a different advantage. They can remain in their territory and continue to forage by simply changing allegiance to the conquering band. They remain alive to reproduce again, whereas the male is killed. OK, so chimps are patrilineal, but what about humans?
Wrangham reviews the ethnographic records, studies of modern-day primitive peoples, and archeological finds to show that humans are, and always have been, a patrilineal society, regardless of what some feminist organizations assert. ... It has been argued that this patriarchy is a cultural invention, but a new field of study, branded evolutionary feminism, views patriarchy as a part of human biology.
Though this makes sense, as I don't recall knowing about any matriarchal societies, besides made-up ones. I often hear that Jesus called God "the Father" because the society he lived in was patriarchal. Maybe it would be more accurate to say the humans species was, and still is.
But perhaps humans are better at psychologically reversing this natural emergent property by simply being conscious of it and making a mental effort to do so. But I imagine that would be pretty hard unless the society was comprised entirely of females. The farthest we could get is to create a completely equal society that was neither patriarchal nor matriarchal. I imagine that would still be pretty difficult though.