If you ask a biologist, you will find that categories like "woman" are not clearly defined. Even the concept of biological sex is really complicated. If you want to pretend that this stuff is all black and white, that's up to you but its not a scientifically literate perspective.
That's not the same as saying that "everything is defined by society/culture?" That's a strawman - no-one was claiming that.
> When biologists claim that sex is binary, we mean something straightforward: There are only two sexes. This is true throughout the plant and animal kingdoms. An organism’s sex is defined by the type of gamete (sperm or ova) it has the function of producing. Males have the function of producing sperm, or small gametes; females, ova, or large ones. Because there is no third gamete type, there are only two sexes. Sex is binary.
> Gender ideology seeks to portray sex as so incomprehensibly complex and multivariable that our traditional practice of classifying people as simply either male or female is grossly outdated and should be abandoned for a revolutionary concept of “gender identity.” This entails that males wouldn’t be barred from female sports, women’s prisons or any other space previously segregated according to our supposedly antiquated notions of “biological sex,” so long as they “identify” as female.
> But “intersex” and “transgender” mean entirely different things. Intersex people have rare developmental conditions that result in apparent sex ambiguity. Most transgender people aren’t sexually ambiguous at all but merely “identify” as something other than their biological sex.
Once you’re conscious of this distinction, you will begin to notice gender ideologues attempting to steer discussions away from whether men who identify as women should be allowed to compete in female sports toward prominent intersex athletes like South African runner Caster Semenya. Why? Because so long as they’ve got you on your heels making difficult judgment calls on a slew of complex intersex conditions, they’ve succeeded in drawing your attention away from easy calls on unquestionably male athletes like 2022 NCAA Division I women’s swimming and diving champion Lia Thomas. They shift the focus to intersex to distract from transgender.
Ironically, "trans women think they're women but I think they're wrong!!" is by far the least real problem being discussed here. Nobody's forcing you to have a nuanced discussion about gender. You asked how we define "woman"; this the answer.
Alternatively you could actual engage with the substance of the argument?