Well, I fundamentally agree with this, with a couple nuances. I don't think the establishment of a patriarchal order is the result of a willful effort from men to oppress women, but I rather think its roots are inconscious, as a remnant of animality in humanity (for such reason, many women can be themselves defenders of patriarchy). Also, I think men are often victims of the patriarchal order, since, just like women, they are assigned an "essence" and are forced to abide to certain canons of virility. While the oppression might be less brutal (because economic and social success is easier for a man), it probably causes sufferance among men as well.