Oh I agree with you on why it’s a bad thing. But the truth is, it doesn’t matter. What matters is that it is happening; just do a search for “I don’t need feminism”. And once a mind is made up it’s near impossible to change. (I assume you’ve been on the internet a while, so you know what I’m talking about.) Each belief is supported by another belief until you get to the core where the only reason for holding a belief is “It feels right”. It’s all emotional. So the only real way of changing these believes is by having an emotional experience.
To many, ‘feminism’ now has negative emotional associations. Why or how that happened won’t change it. We can trust that life will give these women the emotional experience needed to embrace the word feminism, but you know what? I’d rather that didn’t happen because it is very likely to be an experience I wouldn’t wish on these women. I don’t mind removing the label and pasting something else on the idea. It’s just a word. Word meanings change over time. The concept, the idea of feminism will be the same no matter what we call it. <quote Shakespeare here if you wish: “What’s in a name…” This argument is an old one, too> Yet a name is enough for someone to do a mind trick and embrace the concept, or reject the concept.
It’s not rational. That is the whole point, emotions aren’t rational. Same with the “not all men” you mentioned. Men feel bad about the ‘yes all women’, because somehow they feel it puts them in a bad light. They feel attacked and go on the defensive. Nothing rational in that response, it’s all emotional.
I know a lot of women are tired of doing the emotional labor. And rightfully so. Still, we can apply some of that skill on other women instead of pouring it in men only. The term is turning them off. Trying to make them see how they are wrong is going to take a lot more effort than putting a different term, one that creates less of an emotional reaction, in its place.