Specifically the word "woman" pertains to those human beings with XX chromosomes who have the biological design* to produce babies.
It doesn't. We are already have words for that and they are pervasive in this thread; used by you in fact - 'biologically female'. Some biologically female women whose chromosomes are not XX have 'produced babies'. Typically females are XX and typically they are women because they typically are congruent. Same for XY people, ie biologically male, and happening to be men.
It is not only society that creates diversity nature does it too. While people generally accept that nature creates diversity, but dislike it when society does so. Why should some people dislike diversity when nature itself creates it?
There are those of you on this thread who do not accept trans people but make statements such as 'women think differently to men'. Is thinking a binary too? If my niece thinks differently to me about herself, are you saying that her thinking must be wrong? Are you advocating thought policing people? Advocating conversion therapies? Will this thought policing and advocacy of conversion affect me as a gay woman?
If women don't think like men, then should it needs to recognised that people who are chromosomally not XY, who do not think like men, but think like women - what could we call such a condition? Gender incongruence? That being the case, do we ignore the brain as biology and concentrate on genitalia and gametes, the invisible factors such as DNA, and chromosomes?
When we die, the determination of death is brain death, not determined by any of the factors you and others love to repeat. So in this binary advocacy, does the brain trump genitals, or are the genitals 'just everything'?