The Smithsonian and most other major scientific bodies place the first war at 10,000 years ago, a mere blink of the eye in the course of human history. And even then, there was very little warfare until about 5k years ago. Hierarchies exist in patriarchal dominance hierarchy cultures - which only began to arise about 5k years ago. Must hunter-gatherers avoid potential conflicts, as do most mammals, to be honest. You seem to have gotten a lot of your ideas about anthropology from a pop-science book that's mostly false. There's literally so much wrong with that stupid book, that I don't have time to go into it all, but here's a brief piece on some of it.
As noted in the OP, "The new neuroconstructivist perspective of brain development emphasizes the sheer exhilarating tangle of a continuous interaction among genes, brain, and environment. Yes, gene expression gives rise to neural structures, and genetic material is itself impervious to outside influence. When it comes to genes, you get what you get. But gene activity is another story: genes switch on and off depending on what else is going on. Our environment, our behavior, even our thinking, can all change what genes are expressed. And thinking, learning, sensing can all change neural structure directly."
In other words, different experiences, different circumstances, different socialization can all play a part in how genes express. But the whole piece is literally about whether or not "male" and "female" brains exist. The word brain is mentioned in both the title, the subtitle and nearly every paragraph of the essay. Edit: Having a menstrual cycle or a penis doesn’t change the inherent properties of the brain any more than it does the inherent properties of the kidneys or the liver. We might have different outlooks or experiences in life because of those things, but they have almost nothing to do with fundamental brain biology.
A key element of masculinity in our culture is to not be "a girl" which is why so many slurs for men involve referring to them by feminine terms. It's not something that is really in dispute. Trying to make a point about something that I haven't actually asserted comes from reading to respond rather than reading to understand.