Ok, I'm not interested enough to read an entire book. Thanks for the recommendation. Is there no way to have a conversation on your article without me having to go read a book first?
I'm not sure what you mean by partnership. It would be helpful in your article if you could define the roles and responsibilities of each gender in the "partnership".
Anyway:
The definition of Matriarchy from Oxford:
a system of society or government ruled by a woman or women.
In an egalitarian society, the roles men and women have are interchangeable. Either have leadership roles based on merit alone, not gender.
It sounds like what your saying is that things would be different if women (as life givers) were ruling because they are innately kinder and less oppressive. That sounds like superiority to me. I suspicious of anyone who claims that one gender makes better leaders than another.
Again, what's wrong with equality? Why must one gender rule over the other?