I think you're right here, the problem is, this is true of absolutely everything, no? Can you give a definition of a chair that excludes tables and stools and even, as I saw recently, horses? Couldn't we make the same argument with cars and trees and dogs? The difference is, politicians are not afraid to give definitions of these words. And even if they're not 100% perfect, they work in 99% of cases because we’ve commonly agreed on what the words we use mean.
I agree with you that this has become a politicised question. A “gotcha” to try to trip up politicians. The question is, why? Why have so many people made trans acceptance and support conditional on their re-definition of the word "woman"? Why are we bickering about this word rather than the genuine issues and discrimination that affect trans people? I'm sincerely asking. I follow you and really appreciate your perspective on these issues. This one really baffles me.