Recall that anthropological speaking, Matriarchy is different than what we call patriarchy.

When I said matriarchy in the previous comment, I was referring to dominance hierarchy in which women are the top tier and hold power in all spheres over men. A true opposite of "Patriarchy", which is a bit of a misnomer in common language use to describe a patrilineal dominance hierarchy where all power and status go to men.

But in an anthropolical sense, Matriarchy is different because it's not a dominance hierarchy. It's much more egalitarian in nature.

Agree the terminology can be confusing; as always happen when words mean one thing in a scientific sense and another in a street sense.

Hopefully this explanation clears up the confusion though.