You cannot tell people that they have to be a woman or man, it's genuinely does not work.
But it does work, doesn't it?
It's very obvious, statistically.
The men who say they're women behave, statistically, like men, in terms of most obvious sexed differences - sexuality and criminal behaviour.
And the women who say they're men behave, statistically, like women.
This is so statistically extreme that it's a pretty safe bet that any news report of a "woman" committing a violent crime is actually a man who says he's a woman.
Men who say they're women are rare, but women who commit violent crime are even more rare, so the odds favour the former. Because they say they're women, but behave like men.
Your "people say whether they're women or men" model is clearly inferior to the "are they actually women or men" model.
Progress is made by increasing predictive power with a better model, not decreasing it with a worse one.