I have to stop you right there when you say "with these definitions". You provided no definitions. You did commit the fallacy of circular reasoning.

Can you say what they are identifying as without using the word you are trying to define? If you can't then you are unable to provide a definition. But, if you get past this hurdle, you are then stuck with the problem of having to answer this question: then, is it just imaginary?

Finally, in order to get reasonable people to use your non-definitions, you have to answer how your shifting of a meaning, from the observable and quantifiable to the imaginary, serves us, not you, better than the existing definitions where woman is an adult human female and man is an adult human male. It serves society to recognize that very nearly all humans have unambiguous body types that fulfill the needs of our sexual reproduction where two and only two sexes must be paired for reproduction. The two different body types are very different, and women (actual women, adult human females) are vulnerable to violence from men. Changing the definition puts women, actual women, at risk from men pretending to be women regardless of the nature of that pretending. Sex is about reproduction, and each of the two and only two sexes serves one and only one of the two and only two roles in reproduction. Your non-definition can not serve any real purpose for anyone outside of their own imaginations and trying to make others live in accordance to your imagination is, possibly by definition, delusional.