I really want/need to believe that there are social solutions to societies' gender-based issues.

Maybe, rather than thinking about this as inborn vs socialized, it's more like the biological basis of human behavior provides a certain range of ways that people tend to be, and, based on that plus environmental conditions plus prior (pre)history, societies develop and some of those societal manifestations manage to amplify the worst or the best of humankind.

(my round-about way of saying patriarchy sucks, but other forms of society have the potential to suck just as much)