I would also argue that if you're behind its underlying goals, getting caught up in semantics is the real way to hinder progress.
"Well, you've just lost me on the wording," is a classically not-even-coded-way of saying, "I don't think the cause has much merit."
If semantics was irrelevant, it shouldn't matter what we call things. By insisting on calling the US a patriarchy, you are already acknowledging that semantics is relevant. Or are you fine with calling things by any word we choose?
Secondly, the choice of words carries social and political influence. That's just the basics of sociology, for crying out loud. "We live in a patriarchy" has stronger connotations than "We live in a society where men have slightly more power," so it creates the impression that the problems are bigger than they are.
Thirdly, if every country in the modern world is a patriarchy, it places countries like the US and Saudi Arabia as equals in this. But then, what word are we supposed to use if we want to make the distinction that Saudi Arabia is far worse? Super-patriarchy? Uber-patriarchy? That sounds comical.
And, for the sake of consistency, would you be fine with calling the US a theocracy too, then? Religious people have more social power than nonreligious people, do they not?
And where do we stop with this? Should we just cut to the chase and call it a nationalistic militaristic totalitarian plutocracy?
Basically, yes. Those are feminist issues. The problems that face men in terms of custody, reporting abuse, and even more existential problems such as harmful images of masculinity, all tie back to the same harmful binaries: Women are the mothers; women are weaker, etc.
Because more of these issues negatively impact women, and because men, despite facing negative impacts in certain areas, control the overall power structure, we call this movement and perspective "feminism." But it's gender-egalitarianism. Its name is only derived from the lesser of the two binaries. The binary itself is the problem.
Unfortunately, people in this very thread, calling themselves feminists, have openly said that men should stay quiet about their gender-related problems because they are statistically smaller at group level and because men are responsible for the problem at a group level. That's what people have been arguing against here, not ideal feminism.
By the way, I prefer choosing names that reflect the underlying logic rather than the weaker binary, which is contingent, but I won't go to details here.
"Men's rights" get ridiculed because men with an awareness of the larger issues, and who actually want to see results, would really be feminists. They're welcomed in those discussions too. As a counter-initiative, "Men's rights," as you may know it from the Internet, is founded, if not completely on misogyny, on a very myopic perspective.
Unfortunately, people in this very thread, calling themselves feminists, have openly said that men should not be taken seriously in discussions concerning women's equal rights. That's what people have been arguing against here, not ideal feminism.