Patriarchy isn't something that just happens because of some evil hormone, gene, or DNA.

Somebody always constructs the bioessentialism strawman in this kind of discussion, even though literally nobody has blamed testosterone or chromosomes.

It happens through a complex society structure that enforces it.

No, it happens because men are using a complex social structure for the subjugation of women and all other non-men for its intended purpose. For subjugation. They use patriarchal modes of opression to extract labor, to violate, to silence. Patriarchy doesn't just happen. People actively practice it, people derive material benefit from it, and other people suffer from that because we are exploited, undervalued, used and pushed aside.

Trans men are not inherently more prone to patriarchy then anyone else. Given certain types of feminism likes to ignore the truth of women especially white women who uphold it themselves. (This has been studied to death).

Patriarchy, famous for its gender neutrality. Do you hear yourself talk? Yes, i get it, there are women that participate in patriarchy. Patriarchal structures can be used by women to hurt other women, and they are used this way. And yes, white women use it to hurt women of color. Cis women use it to hurt trans women. Trans women use it to hurt other trans women. All of that is true.

But none of that changes that patriarchy is, at its core, a system that allows men the opression of women.

Why do you have to distort the nature of patriarchy like this? Why do you have to completely obfuscate who it materially benefits the most? Because these women who collaborate with men to uphold patriarchy aren't the ones who get the most out of it, they are still below men that share their class, race, etc. A white woman who becomes a class collaborator in the system of gendered class violence and upholds patriarchy exchanges servitude to white men for the limited privilege of ruling over women of color. She is still relatively marginalized even when she upholds patriarchy. She participates in a system that exists for the benefit of men.

And on top of that, it is blatantly obvious who commits the majority of patriarchal violence. It's men. And they mostly harm women and other people who aren't men.