I don’t believe they are defining of your sex, or even determined by it.
I think, without going all Shania Twain, that you can feel like a woman. You can observe and live in the world with a female outlook, which can and often is different to the male lens.
I also believe that you can therefore feel that you are living in the wrong body, because you are looking through the wrong lens if you will.
I’ve always, maybe wrongly because I’m not trans, assumed that being trans felt like being trapped in the wrong body. Your sex and biology was telling you that you were male, but your brain and emotions were telling you otherwise. That must be horrendous. Locked in a body you’re not comfortable and don’t feel at home in.
I’m not big on the “single sex spaces” argument anyway, personally not interested in it though I have obviously seen and recognise that others are.
But, with no idea on how you’d police it, if someone feels the way I’ve just described above and they want to transition their gender identity to that of a female - I’m cool with letting them.
That doesn’t change biology, scientific fact, but I don’t see any value in making people feel worse.