Prawnofthepatriarchy Yep. For you to accept this definition you have to accept that gender identity is a real thing, which you don't. So possibly a non-starter. We've been round the houses on this a number of times.
OK - definition of a women, based on WHO, NHS and other human rights and medical bodies, tweaked by me. I won't go into depth on stuff you'll agree with.
Sex - female, male, intersex
Cisgender: means that your sex matches your gender identity.
Transgender: If your sex does not match your gender identity, then you are transgender.
Gender Identity: Gender identity is the sex that a person "identifies" with or feels themselves to be. While biological sex and gender identity are the same for most people, this isn't the case for everyone. If your gender identity matches your sex, you will not feel a sense of incongruence, and you are cisgendered. Much like sexuality, you can't point your finger at a location for it and it's innate. It's not a belief like a religion. [Here is where all the fighting between GC feminists and transactivists happens]
Gender expression is the physical manifestation of one’s gender identity. It's culturally conditioned and often oppressive. Some people's gender expression matches the societal norms for their gender. Some don't. Wearing pink doesn't make you a girl. Climbing trees doesn't make you a boy. You gender expression absolutely does not have to match your gender identity.
A women, then is either a female person who is cisgender, or a male person who is transgender
This definition excludes a bunch of other genders, but baby steps.