I just want to part ways by saying that although social stratification (class systems) of all sorts are key to patriarchal dominance hierarchies, gender stratification absolutely is a vital aspect of this too and has been for 6 thousand years or so. I can attest to this both as a social scientist and as a wealthy white women who has been marginalized and discriminated against her whole life based on nothing but my sex - and it continues to go on to this day. Not really all that surprising since a mere 50 years ago women were second class citizens by law in the US. Discounting that because you don't have a lot of personal experience with it is a huge mistake in understanding what's going on. It's not the only aspect, but it is a vital and rather central one.

Cheers!