Biologically, an adult is a human or other organism that has reached sexual maturity. In human context, the term adult additionally has meanings associated with social and legal concepts.
I'm just going to repeat this quote again in it's whole, and let's see if we can't see that this is exactly how a lot of people see the definition of "woman".
All the other shit is gender
Ah, gender. The externally observed set of stereotypes that represent one sex or the other.
Why do you think people exhibit gender, usually in alignment with their sex? My understanding is that people are drawn to "signal" their allegiance to particular groups by exhibiting the stereotypes associated with that group.
Useful for reproduction and social function.
Also there are benefits to rejecting the stereotypes associated, not least these days the desire to be "cool" or subversive, or simply to reject them when associating with that group serves no particular function for an individual.
Seems there might be something inside some (each?) of us that draws us to interact with (either through acceptance of or rejecting of) the stereotypes associated with our sex. Some people call this their "gender identity".
Gender identity, then, would seem to have quite a fair bit to do with who gets to be "socially" a woman, don't you think?