self-identified gender overrides biological sex
That is not at all what the argument is. Rather, the argument is that the biology of sex differentiation is extremely complicated, insofar as many things can end up many ways in any individual.
Trying to reduce it to just one part of biological differentiation is naive, especially when genitals don't do any of the thinking, and only express the directives they may upon behavior through a single, easily hijacked chemical pathway.
What is more important behaviorally, is which of those pathways are being leveraged.
I'll tell you what, I certainly didn't need testosterone to feel like myself. The thing is, some people DO need it to feel like themselves. And some people need estrogen to feel like themselves. It's a hard thing to explain to someone who doesn't understand what it's like to be taken away from yourself by hormonally influenced parts of your own brain.
And when I feel like myself, the fact is, I don't feel like "he".
I'm not a "she" either.
I think I have an interest in "drag", insofar as I very much would like to be able to afford some nice dresses tailored for my body. I expect a great many women and men have similar interests of dressing up in a nice dress being dressed beautifully, like a flower to be appreciated for a time.
But just like Toni wearing pants does not make her a man, and never should be construed to, being interested in that is not something exclusive to women.
And, I think it's important for kids to know that if they grow up and want to wear a dress and feel pretty for a while, that's OK no matter what the worst parts of our culture may say on that matter.
What drives me to identify as "they/them", however, is not the desire to wear a dress and feel pretty. Instead, my identification is driven by the fact that I reject the influence of testosterone on my brain.