The anicient Kush society isn't evidence of much, we don't know enough about what day to day life looked like there. We do know that in many matriarchal societies we know about more clearly, like the Iroquois, men were still mainly responsible for things like warfare.
We also know that among many other mammals, males are more aggressive overall. That doesn't mean they are never gentle, nor that female animals are never aggressive, we aren't working in absolutes here. But it's universally accepted in biology that this is a thing, and humans are not somehow outside of that.
Where biological determinism and free will intersect, in human beings, is a difficult question. St Augustine, living in the last days of the Roman Empire, maintained that we do have free will, but that it is compromised by the effects of the Fall, so that human beings are subject to original sin to the point that sometimes we can't even know if we ourselves are entirely culpable for certain acts, or were entirely at the mercy of our weaknesses of mind and body. The only solution, he suggests, is to trust that God knows the difference and depend on his mercy for the rest, and go forward as best you can with the assurance that you are saved, if that's what you want. That's in terms of the soul though, he doesn't suggest it changes how the law deals with people.
I'm not sure that modern psychology really gives us a better answer than that.
In any case, given that I am personally quite affected by my own hormonal fluctuations, and have just had to apologize to a friend for over-reacting to a comment which I would be unlikely to have done were I not in the throes of PMS, I don't really see this as much of a controversy.