Your views on how matriarchies can exist is incomplete.

In Atlantis there were rejuvenation chambers.
These were operated by women (by feeling / intuition, which women are much stronger than men in) and required a baby (to tune it)

Thus, the women decided, basically, who would live and who would die.

The "powerful" women lived for centuries.
The working brutes lived for decades.

There are many areas that woman are much stronger than men.
(survival hunting and civilization building are not them)

There are feminine technologies.
We don't really use them.
(imagine an entire field of technology that has barely been tapped, and we think we are technologically advanced)

The thing i really hate the most is that women had the choice. They created men. Gave them all the shit jobs, while keeping all the good stuff for themselves.

To see this look into lizards. There are many female-only species. They don't need no man. But, the lizards that have a male/female do far better. The men are stronger than any "woman", better at defending territory and hunting. So, the male-female species will drive out the female-only species.

And yes, females of earth decided this split long ago