Different people mean different things by "patriarchy". You've given enough hints so that I think I know what you mean by it, but do you have a definition handy so I can be more confident?

The reason is that most of the discussion around this (not by you, but on Medium in general) seems to be based around linguistic conflation of two different things, one of which is really problematic but mostly isn't true any longer, and the second of which is very workable-within even if not ideal but still is true. The linguistic sleight of hand is that people pair the existence from the second with the badness of the first and end up wielding a non-existent chimera that motivates highly counterproductive drastic actions.

(Also, you don't seem to have provided any support for the claim that backlash is the explanatory factor. You seem to have just restated that it is. I, too, can restate my point without further evidence! See: no, I checked, and as an explanatory factor, "backlash to women gaining equal standing" doesn't work. The timing is wrong, the scale is wrong.)

Also you're still doing the "we" "you" thing, where you're slicing things up by gender.

My "we" is all reasonable, compassionate people who want to have a society that enables as many people as possible to have fulfilling lives. I reject as bigoted your apparent inclination to assign my relevant characteristics as "you = man". This is not the relevant distinction to make between people most of the time (and not this time). There is strong psychological support for the idea that othering leads to a loss of compassion and greater tolerance for anti-social behaviors. So, not gonna do it. I'll discuss issues relevant to group boundaries as necessary to understand systematic lack of compassion, because lots of people do other across identity group boundaries. But I don't view you as "a woman" but rather as "Lorelei Weldon", and if I think you're mistaken, I'm not going to paint (my perception of) your mistakes over all of women, just over you and anyone who explicitly assents to the same view.

If patriarchy is a problem, it's not "men's problem". It's everyone's problem, because we're in society together. If society is organized in problematic ways, we all need to solve it. Does this mean men might need to do things differently, including some difficult/uncomfortable things? Yes! Does it mean that women might also need to do some things differently, including some difficult/uncomfortable things? Also yes! Would I guess that men probably on average would have the larger share of the work? Yeah, probably. But it's everyone's problem.

Abortion rights? Everyone's problem. Football head injuries? Everyone's problem. Girl-girl bullying in schools? Everyone's problem. Anti-vaxxers? Everyone's problem. Prostate cancer? Everyone's problem. It's all everyone's problem.

The point of first wave feminism was that women should be partners in shaping society. It's a much better way to organize a pleasant society now that we have the technological mastery that renders most of our intrinsic physical differences irrelevant and a social system that resolves almost all issues without resort to fighting despite scaling to a vast society of mutual strangers.

But that means you are expected to do your part, which is more than just to tell men to fix it (especially post-second-wave). The first step is to stop making things worse, please (at least on Medium...elsewhere maybe you're making things better), and then maybe some improvements will be possible.

Unless you wanted to provide a case study in action to highlight Simon's point. Then, yeah, okay, very sneaky, and good show!