Historically, pregnant women and women with small children faced much more difficulty capturing and maintaining adequate resources on their own. Predation, lower upper-body strength, releasing a scent for one week per month, not to mention the metabolic and time constraints created by nursing and mothering small children in general, all created huge, difficult barriers to survival for women.
Historically, men were able to gather more resources from the environment than they needed (primarily through hunting, but later through farming), so they could share their resources with the women and children. However, men didn't want to share their resources with the genetic offspring of other men, so they wanted monogamy in return for support.
At a high level, men gathered resources from their environment, and shared them in exchange for monogamy and adequate care for their offspring, and women, historically, gathered resources from relationships (with both men, for food, shelter, and protection, and from women for child care and protection).
This is the main cause for differentiation between men and women. Because of this division of capabilities, the brains of men and women began to differentiate and evolve because they faced different challenges in their environment.
Men needed to be able to hunt, to work, to go without food for longer periods of time, and to work as a group to hunt large game. Testosterone helps all of those activities. Those who were more successful at these activities had more progeny that survived.
Women needed to be able to successfully raise children, gather local food, process furs, and cook food.
Men would all go hunting together in groups to reduce/eliminate opportunities for philandering, and women would stay in groups to protect each other and to help care for each other's young.
This all got flipped around and mixed up by the industrial revolution, the world wars, antibiotics, vaccines, and birth control. IMO, this is the battleground of the current culture war, because for most of human history, resources were scarce and infant mortality was high. These arrangements have been in place for hundreds of thousands of years.
The recent change in access (and abundance) to resources I listed above (among many others) has fundamentally changed access to resources. As an illustration, the most pressing problem facing the poor class in America is obesity. This is unprecedented, and no one has a good guide for how to move forward.
These characteristics would have predated humans. Maybe pull the terminology back to male and female hominids in the future?