"A woman is misclassified as a man, finds out and corrects it" is a more useful approximation [...] and is closer to the motivation of transpeople than the "choice to change" one.

I understand that some people don't model themselves as being sufficiently agentlike to admit that their major life choices were in fact choices; it's certainly politically convenient to claim to have an immutable innate identity that everyone needs to respect. But other people who do model themselves as agents---sometimes even genuinely dysphoric people who might partially understand a little bit of what you're going through!---might have an interest in defending social norms that let them describe their model of reality in non-contrived ways, even if that occasionally hurts some people's feelings. You can and should edit your body and social presentation if that's what you want to do. You cannot edit other people's models of reality, and people might push back if you try to shame them into doing so.