Patriarchy is a social system based in a dominance hierarchy. It has an element of men controlling and having power over women, but it's primarily a wider system of social stratification that is maintained by intimidation and violence. We absolutely live in a patriarchy (and I know you've already read my story on that, so I won't link it again). That is the appropriate sociological term.

I feel sorry for the way the woman you described had internalized these aspects, but it's not surprising given what you said about her upbringing and about the culture more generally. We're all swimming in that ocean and it takes guts to choose not to buy into that system. Women absolutely uphold patriarchy as well, or it wouldn't still be in place.

https://medium.com/inside-of-elle-beau/women-uphold-the-patriarchy-too-c6c2e5de8619

"How paternity came to be central after it wasn’t for 97% of the existence of Homo Sapiens is way beyond what a blog post can address. What is important to note, though, is that once paternity becomes important, controlling women is inevitable, because only by controlling women can it be reliably known who the father is. There is an irreducible distance between the biological father and the offspring that can only be eliminated fully by imprisoning a woman and preventing any other man from having access to her. This is why patriarchal societies by necessity become societies of control and separation. We have become so habituated to this state of affairs that most of us don’t even see that it is our own creation.”

Many women uphold patriarchy, despite the ways that it disadvantages them, because of the ways that it feeds into greed and fear but also an unwillingness to pay the price for bucking the system. Misogyny is the policing arm of patriarchy, and women who deviate from what is expected of them by patriarchal standards often find themselves facing censure and punishment for that — from men but also from other women."