It looks like the discussion at least got as far as acknowledging that "patriarchy" is a social, economic and political system rather than individual people or groups of people. That's why the opening post didn't make sense.
Imho, our society embodies patriarchal principles, but also white supremacist, non-disabled and class privileged and heterosexist principles as well. Patriarchy doesn't really cover all that, so I actually favour the concept of "kyriarchy" (although I'm aware some folks don't like the name, but it doesn't bother me much and it's the concept that's important here.) All the systems are linked and intersecting, and because people's identities and experiences don't fit into neat boxes, I think it's important to understand that complexity.
I think someone above alluded to the fact that some women can hold privileges within a patriarchal and/or kyriarchal system. For example, a white, class privileged woman may may benefit from her proximity to and relationships with white, class privileged men. Her father may have paid for her to have a top class education. Her husband may have the resources to pay for childcare so she can pursue a profession she enjoys without the need to earn a living wage. Neither necessarily seem like privileges until you realise, for example, working class white women or women of colour are unlikely to benefit in the same way through their proximity to or relationships with men in their lives who, like them, have limited resources or don't benefit from white privilege.
I think the OP might have been trying to ask whether even men who don't actively want to have privilege also benefit from patriarchy, and yes they do. As a white person, whether or not I ask for it, I have privileges because I'm white in a society that is institutionally racist. Even when I try not to collude with that privilege, I may not even be aware I'm exercising it (until I discover a person of colour can't take for granted what I can.)
However, I could go on a march against a fascist organisation, or challenge other white people when they make racists remarks. I might be putting myself at some personal risk in doing so, but if I "let things slip," then I am indirectly colluding with the mechanisms of institutional racism. Same goes with a bloke - they can choose to challenge other men on their privilege, could get punched for it, but if they don't make a stand, they're still shoring up the structures of patriarchy with their silence.