I disagree with you that they're afraid of it. As you said, power comes in various forms and those other forms are not a problem.
I think a lot of them don't understand it. We've been without it for so long in male/female dynamics, there's widespread ignorance of how to wear it.
Religion is a huge part to play. Funny how that works.
I think many don't trust it, even if they sort of think a matriarchy is better. They might see the idea as a trap of some kind, usually to dump more work on women or to blame women for when things get bad. They're going to. A matriarcby that pushes and demands man/woman pairs on those who want same sex pairing or to not pair or group bonding is not going to be any better than patriarchy just because it's more benevolent. There's a problem with marriage specifically. If a new arrangement doesn't fix that, that problem will just degrade the matriarchy too. Stuff like that. A