Scrumplestiltskin - I didn't say that trans people are in the same grey area, would indeed never do so, just that there is one. And the existence of one undermines the concept of neat binary boxes for biological sex.
No, actually it doesn't when it comes to people who actually do fit in the "binary box." The existence of people with disorders of sex development (that usually result in sterility in fact,) has no impact on people with normal sex development, or relevance to them.
It's perfectly valid to say that a particular subset is within a set without having to fully define the boundaries of the superset.
You haven't defined anything. As far as I know, you define woman as "someone who wears pink". You haven't defined subset, set, or superset. You've given us less than nothing.
I don't think I've heard a cohesive definition of woman from you either. So far you've variously differentiated by:
Genitalia
Chromosomes
Assignment at birth
Chromosomes dictate reproductive systems and genitalia, except in the case of intersex people, where birth assignment based on phenotype or condition is what dictates the sex class they are placed into. Seems coherent and cohesive to me.
Chromosomes dictate reproductive systems and genitalia, which in turn dictates sex. (After all, sex only exists for the purpose of reproduction, doesn't it?)
Additionally, there are intersex people who do not fit either category neatly at birth - who are the exception to the chromosomal and reproductive system rule due to their disorders.
Females are also not born with a penis (chromosomes = reproductive sex,) and in our current society receive female socialisation. So again, what's not coherent about that?