There's nothing ineffable about being a human female, humans both male and female have been able to recognize which humans are female (and treat them as lesser as a result) for millennia.
I see you left out the word "adult" from the "woman" description (adult female human), probably because that's the ineffable bit.
Someone was always going to notice.
So here's the thing, "adult" has a biological meaning, as in the age of sexual maturity. It also has a legal meaning, an age in years, which varies by country and is not the same as the age of sexual maturity. It also has social and personal meanings; behaving like an adult, feeling like an adult, what it means to be an adult; and quite aside from the legal and sexual side of things there is a wide understanding that it can be some self-identified point in an individual's own life that could not objectively be defined.
Perhaps I became an adult when my mother died. The concept of that certainly isn't alien to anyone. No-one's going to shout at me that "Adult is the day you turned 18! There is no internal sense of adult! Legal adulthood is a social construct!" - because that would be silly, and in complete denial of what we use the word to mean.
The law seems to work just fine with that.
It's a complex and nuanced concept, but we're coping it would seem.
To me, "woman" is the same thing. It has a biological meaning, a legal meaning, a cultural and social meaning AND a personal, internal meaning for some; and the reason I know it has a personal, internal reason for some is that they tell us so - and that is how we come to know these things.