This is my impression, too, but I will read the book to learn more.
Still, I am wary of anyone who argues for patriarchy as a feminist solution, given that it is explicitly hierarchical, with men ranked above women in law, religions, and so on, and given that we see what extreme patriarchy looks like in Afghanistan.
Even in less extreme versions women have fewer rights and less agency and power than men, so it's hard to see how the system could be argued to 'balance' the needs of the sexes unless women are seen as inherently submissive and happy to be subjugated in some forms.
I presume that it's possible to argue that patriarchy as a social arrangement somewhat cares for the needs of both sexes (though mostly for the needs of men) if it is only compared to some chaotic lawless society with marauding male gangs when even widespread domestic violence by one male might be preferable to violence by many strange men.
But that is a dismal view of the possibilities which societies contain, and the development so far has been very much away from patriarchies. It's certainly not a feminist proposal, to bring patriarchies back even more widely than they currently are.