I'm not quite sure of the question, so I'm not quite sure how to answer.
I can say a few things though:
There have been very few genuine matriarchies in recorded history, and not a single matriarchal culture has developed a notable civilization, much less a great one.
Neither the United States, or Britain in recent centuries, has been a patriarchy. In fact, the British Empire and the American empire are the great civilizations that have come closest to being a matriarchy, so calling these civilizations patriarchal is exceedingly ignorant.
Blaming patriarchy or blaming men for all the ills of society is exceptionally sexist. Men certainly have their share of blame, but women have their share as well - and in fact we know that women are slightly more likely to abuse children than men. Most men care about the well-being of children, both their own and others'.
If we want to create a better society, it will have to be more patriarchal, not less. Not that men have to dominate, necessarily, but right now the balance is shifting to rule by women, and it obviously isn't working out. Judging from the success of past civilizations, we will need to have at least a balance of male and female power, and possibly a slightly patriarchal society - because that is what works best for both men and women.