You probably already have, you just didn't realize it.

Interesting that you're willing to believe there is a matriarchy but unwilling to see a patriarchy.

If you read my comment through more carefully, you'll notice I did say that women have and do participate in the system too.

A dominance hierarchy that places men in positions of primacy socially, economically, and politically is a patriarchy. That's the organizational scheme we live under. Here in the US, the economic primacy has been legally lifted with the end of coverture laws but that's only been during my lifetime and women are still working their way into full economic enfranchisement. There are still hurdles to cross.

Politically, the opportunity is there, but much of politic is bound to social beliefs and constructs. It's harder for women to get elected into office when so many men and yes, even some women, still believe women don't and can't make good leaders. They're also less likely to get funding support and election bids cost money. Hurdles.

Socially men are considered more important and of higher value. Men will argue this because women have that "inherent" reproductive potential. But I would counter with the observation that that makes our wombs valuable. Not us.

The patriarchy is alive and well my friend.