The differences between newborn male and female brains are very small and you declaring “it’s been proven false by science” doesn’t belie the fact that this is far from settled. Plenty of scientists feel differently.
Yes, women as bearer’s of children, particularly in a time before formula, does mean that there were some gender-related elements, but in pre-patriarchal societies, women were doctors, judges, priestesses, etc. And what exactly is your point anyhow, that people should be boxed into roles and lanes based on their biology?
And you still haven’t accounted for the fact that men in other parts of the world have the same hormones as men in America, and yet many, many of those countries do not have the same statistics about violence.
I’ve got better things to do than go round and round with you on this. 👋