Custody going to women most of the time does not make a society a matriarchy, and a dominance hierarchy isn't the only type of hierarchy. Patriarchy is a dominance-based hierarchy. Telling boys not to fight is not being anti-male because boys who live in partnership-oriented societies such as hunter-gatherer tribes don't fight each other for fun or to establish dominance. Wanting to fight each other is socialized; it’s not intrinsic to masculinity. I would say that it is your definition of these terms that is very inexact and subjective because mine are based on sociological models that have very defined parameters.
I've written on this extensively already so I'm not going to reiterate it here. If you want to better understand what I'm saying, read these: