This may seem absurdly simple but I think it bears stating anyway.
When ideologues insist a woman is someone who says they are a woman, yes they are putting forth a hopelessly circular concept. And they deserve to be mocked mercilessly on that basis alone.
But they are also making an admission that someone’s adherence to a gender stereotype dictates whether they are a woman or man. And this needs to be called out too.
Typically in the “what is a woman?” dialectic, the GC side will rightly point out there is no answer gender ideologists can give that is not circular or stereotype-based. I recently had the epiphany that the circular definition is stereotype-based. It’s just less obvious than traditional stereotypes.
When we say men are women if they assert that they are women, this is another way of saying males who “do what women do” are women. In other words, their behaviors conform to what is generally ascribed to women, and therefore we should label them as such. Not much daylight between this and labeling men as women if they cry at the end of sentimental movies or enjoy knitting. As long as a person’s actions are sufficient to place them in a gender category—in this case, the action of self-identification—then the definition of that gender category is grounded in stereotype.
Progressives who parrot TWAW may very well tolerate looking illogical, just as long as they feel like they are scoring “be kind” social justice woke points. But it’s harder to maintain a self-image of righteousness when you’re forced to see that you’re illogical and regressive. They want to say it’s wrong to reduce women to reproductive biology, but they are reducing women to the stereotype of identifying as women. There is no valid defense for this.