As in, the substance of the argument is less important than the parties involved.
As in, "So women have special interest groups and dedicated clubs? Fine. Then it's OK for men to work to get their seat at the table, too." This explains a lot of the eagerness for leaders who know how to "fight". It also explains the lack of caring around ideological hypocrisy. It's like lawyer logic on some level:
"My client was not in town that night. And if he was in town, he did not borrow the mower. And if he did borrow the mower, it was with the consent of the plaintiff. And at any rate, the mower was already broken. And if it wasn't already broken, it broke itself."
...the important part of the argument is the defense of that particular client, not the logical coherence of the narrative.
To take racism as an example, if you grew being told that racism means race-based prejudice and it is wrong and that one can be racist against anyone but a white person, you say "that's ridiculous".
The actual idea behind that is that racism is more than simple prejudice and crucially includes a societal power differential between two groups. And that race is a constructed concept and very important because society is structured around it, valid or not.
The pop explanation implies we are engaging in collective punishment against whites and men because of current and historical wrongs. That's wrong, but a lot of people on every side believe it. You almost couldn't have designed a situation better to create a new white nationalist and anti-feminist movement if you tried.
It is, to generalize, a group of white, middle class people who were raised in this modern feminist/neo-liberal framework that struggled to translate very academic ideas into a pop culture suitable form. Those poor approximations got mutated by internet forum culture (tumblr and 4chan most famously, but it happened everywhere).
The alt-right people looked at this incoherent pop-ideology and, not totally unfairly, saw it as saying that race and culture are the same and are very real, unless you are white. Sex and gender are the same, are real for men but a constructed form of oppression for women. It's not a fair description of the actual ideas, but the pop-ideology was and is an incoherent mess. So a group of mostly middle class, mostly white and mostly men rejected the parts they didn't like and used the incoherent aspects that benefited them as weapons. The parts they did like remain unexamined, so while they ridicule the language used by their "enemies" they still think inside that ideology.