How does this notion compute with a society where women and men are equal?

You contradict yourself multiple times, in this article; and you also seem to employ oscillating definitions of what a "matriarchy" supposedly is.

It sounds to me as though you lacked critical thinking skills, when you were a kid -- and now, as an adult, you STILL lack them...but you're just overcompensating in the other direction with cult-like sentiments.