Here's the thing - I think "matriarchal" in its historical practice is very different than "patriarchal." In other words, it's not a "flip side," an "opposite" as one would assume. If you look at matriarchal cultures from history, you see that they were, in practice, very equal cultures, but decision-making and social culture was largely determined by the women of the culture. The men in those cultures were not subservient or disempowered.
Whereas, in a patriarchy, the women are considered secondary, are not treated equally, are supposed to be subservient. There is domination in a patriarchy, yet not in a matriarchy.
But the way you said it - which I hear all the time from men (that they are worried they are going to end up under our shoes the way we are currently under men's) - sounds like you were referring to women dominating men. So I think it's important to think about the fact that domination is not typically a practice in a matriarchy.
I don't think it has to be one or the other, though you are right - the pendulum will always swing in all things, which makes me wonder if we are capable of achieving a middle ground.
And it is a worry that so many men want the patriarchy while so many women just want an equal society and maybe that's not enough to right this ship.
I do think matriarchal women are rare - I have never seen a matriarchal family in my life, though I know some must exist. In the middle-class white culture in which I've grown up, I have never witnessed it and I do not know anyone who I would call matriarchal. My family is filled with strong women, but husband/father rules the roost. I found an old home video of my family from 1994 in which someone was videoing my parents and prompting them to say hello to my grandfather, who would be watching the video later and neither said anything, then my mom said, "Honey, say something! You're the head of the household! I can't speak before you do."
I saw that my whole life not just in my family but all around me.
I absolutely think we need an insurgence of women in power - not exclusively - but far, far more than what we have now (America has one of the lowest levels of female representation in the first world, which speaks a lot about our cultural misogyny). I think we need female voices in every single major decision we make as a country and that fact that we don't in 2020 is insane. But I think we would still need to include other voices in that (including men) - though also, I think female leaders would do that, naturally, whereas men typically do not.
OMG, this is so much more than I meant to write. LOL. This kinda gave me an idea for an article, too, if I can flesh it out. Thanks for the discussion. <3