It makes no sense because "gender" as a word has been used both as a way to talk about biological sex without saying the word "sex" and as a way to discuss sex-linked social roles. "Gender theory" was always a poorly defined set of post-modern word games that was then filtered through teens on Tumblr and turned into something even less coherent.

What the kids these days seem to think is that "gender" is an actual essence that people feel and that this essence determines whether people are "women," "men," or "non-binary." It's not the same as sex stereotypes, although people often draw on sex-stereotypes to express their identity. For the true believer, they really believe that people have an innate gender identity of "man," "woman," and "non-binary" that has nothing to do with the body. Thus, when they say women can have a penis or a man can have a vagina, they really mean it. Genitals are arbitrary; the inner gender identity is real. True believers also seem to think "women" and "men" have always been used this way and everyone understands what "women" and "men" mean in this context.

Any reading of history or conversation with a non-too-online person would reveal that no, most of us genuinely have no idea what they mean and no, the words have not been used in isolation from biological sex. Unfortunately, social media has made it really easy for people to form echo chambers. Also, groups like Gender Spectrum have provided horrible puberty/sex ed materials that basically miseducate kids about biology and gender. Their content only makes sense if gender = sex stereotypes, but they do a lot of word games to obfuscate that. (They also misrepresent intersex conditions and appropriate intersex language, but intersex activists get regularly harassed for trying to point that out.)

Modern teens are spending so much of their lives interacting in a disembodied way through the Internet that I think the inconsistencies of gender theory are probably much less obvious to them. Many of them will not have experience with embodied desire, or will have negative/traumatic experiences. Puberty will be making their bodies uncomfortable and unfamiliar. I would guess that the idea of remaking their body to express an idealized inner essence would be appealing.

I think the mechanism for adults is probably a little different, but that the attraction of gender theory is similar. Even though I have to believe every adult over 30 knows in their heart of hearts that gender theory makes no sense, it must be a seductive promise. Uncomfortable with sexism? Feel like you're not quite like other girls? Now you get to opt out of being a woman. (Even though, of course, you don't.)

While I do think there are many true believers or people who are willfully putting on blinders, I also think there are many people who are manipulative. If trans activists really believed in gender identity as they express it, there would be no need for medical transition because woman/man/non-binary are completely separate from bodily appearance. We would also see more arguments for adding non-binary categories and spaces (since otherwise, non-binary people will be excluded or misgendered).