In my experience, universities are populated with manly women and womanly men. I won't claim that academia is a matriarchy, but it might easily reach that point. It seems to attract men who lack the masculinity to compete in other fields. Perhaps aggressive women are drawn to the power vacuum or to the leftist culture.
Many of these women are tough as nails. If they had been running the universities in the Sixties and the student protesters had been, say, neo-Nazis, there would have been a hell of a lot more than four dead at Kent State.