The answer that I have come to is that the term 'woman' is vague, it means different things to different people, and that's ok. Defining a group based on difference like you have makes things needlessly complicated, for example what is chair?:
As we have all come to understand in recent years, CHAIRS can HAVE WHEEL, but CHAIRS can also HAVE LEGS . They can have a BACK, or they can lack them. They can be WELL BUILT or they can be WEAK . They can be strong or they can be weak. They can be short or they can be tall. What does the word CHAIR mean? It seems like a word that doesn't mean anything at all?
A chair is something you perceive as a chair and a woman is someone you perceive as a woman. Thus, to identify as woman means you would like to be perceived as a woman with whatever baggage comes attached with the person's concept of women. To that end you 'do woman'
You sit on it (butt don't take it with you).
Next question, please.
Though you could start calling a particularily comfortable spot "yours to sit on", a kind of proto-chair, perhaps even a throne.
Also, humans have been putting a type of chair on horses for some 2700 years, called a saddle, and sitting on that.