I meant reverse in the sense of it's still based on dominance play. It's matriarchal instead of patriarchal.

You've used that description yourself.

I agree that matriarchal societies are less violent and more caring than patriarchal ones. But, most women don't want that either, it seems, because it's still based on division,"separate but equal", conscribed roles roles and places in society.

Better than patriarchy is better than patriarchy, but it's not perfect just by being NotPatriachy.