Political Memes

First you have to ask what gender is. Gender is a set of behaviors expected of people of a given sex.

Then, you have to ask what it means to belong to a given gender. You don't have to, and can't, meet all the behavioral expectations of a given gender. Those expected behaviors change over time. People of all sexes have interests that cross gendered lines because gender is not perfectly correlated to specific behaviors - instead it is a broad notion of behaviors that are considered to correlate with a given sex.

Additionally, there exist people who are not really male or female due to genetic differences. But, society typically treats them as the gender typically assigned to the sex they most resemble. So, since they do not have the "correct" sex and may not participate in the "correct" behaviors to belong to a given gender, their assigned gender is arbitrarily determined.

Those 3 things establish that gender is: not biological, not behaviorally determined, and somewhat arbitrary.

Since gender isn't biological, woman =/= female person

Since gender isn't behaviorally determined, woman =/= someone who engages in typically feminine behaviors

Since gender is at least partially arbitrary, woman =/= a factual category that can be determined by material features of a person

If women don't have to be female or engage in typically feminine activities and can't be defined by physical or genetic characteristics, then what is left? Someone who identifies as a woman - who wants to be treated as a woman by others.

"But that's circular!!!" It actually isn't. "Woman" as a category confers societal roles and expected behaviors onto a person, "woman" as a person just means someone who belongs to the category "Woman". The only determining factor is being a member of the category. It'd be like asking "what is a boy scout?", getting "a member of the boy scouts" as an answer, and then being upset that there isn't some fundamental universal law being appealed to when classifying people as boy scouts.