So why do so many people believe that you can change sex?
Partly because you can't.
If we could do this, you would see an actual conflict between the men who had changed sex and those who hadn't. It would be like the "tru trans" thing but worse.
And you would have sensible objective rules about how to handle sex changes. It's because we can't do it that we don't know how to handle claims of having done it. We try to pretend that there never was a sex change and that "they were always that sex". Which is where the whole thing disintegrates.
If we could change sex, then we'd try to slot in the trans with the actual sex-changers, subject to their rules. Any claims to somehow get more rights than sex-changers - a pretence of no sex change - would be self-evidently ridiculous.
Obviously a man who had sex-changed wouldn't compete in natal women's sports, for example, so why would a trans male think they should? It wouldn't get anywhere.
They like to talk about clownfish - imagine the fun with trans clownfish versus those who had changed sex. You'd be having endless arguments about what it meant to "change sex" and why the trans clownfish were no different from the sex-changed clownfish.
But because no-one has done it, there's no real pushback to the claim. (Apart from women, obviously, but who cares about them).