There's never been a matriarchal society - except perhaps maybe, maybe in Crete. What we had before patriarchy (which is a form of male led dominance hierarchy) were egalitarian cultures. A matriarchy would be a female led dominance hierarchy, and in matrilineal cultures, what we see instead is balance and a belief that men and women need each other and that they compliment each other.
What caused the shift was warlike, hierarchical, authoritarian, male god worshipping invaders sweeping through the peaceful lands they conquered on horseback and slaughtering all the men and children so they could take the women as war prizes.
The one thing they all had in common was a dominator model of social organization: a social system in which male dominance, male violence, and a generally hierarchic and authoritarian social structure was the norm. Another commonality was that, in contrast to the societies that laid the foundations for Western civilization, the way they characteristically acquired material wealth was not by developing technologies of production, but through ever more effective technologies of destruction.
Eisler, Riane. The Chalice and the Blade (p. 86). HarperCollins. Kindle Edition.
Unfortunately, this dovetails rather nicely with predatory capitalism, with colonialism, and in many ways with Christianity and other mainstays of Western culture. However, Nordic countries like Denmark have found a way to balance a robust economy with more partnership-oriented styles of relating to each other. I'll be writing more about this in the coming weeks, but here are a few things for you to check out in the meantime.