All you're doing is demonstrating how much rubbish it all is.
Saying someone can identify as a different gender to their birth sex is like saying someone can identify as a different star sign to their favourite colour.
Sex and gender are two different things, and one of them is real and the other is imaginary. Why this presumption that the norm is for everyone to have a gender that matches their sex? Wouldn't it make more sense to say, "Hey trans people! Great news! Nobody else has an identity which matches their genitalia either! You're not different. You're not special. You're just an individual, like everyone else. But you also have to live in society, like everyone else, so we can't just exempt you from the rules which apply to everyone else."
The girls were absolutely correct when they said if you have a willy you're a boy and if you have a vagina you're a girl.
If you think what makes someone a boy or a girl is about gender rather than sex then perhaps you could explain to us all what the fuckity fuck you understand gender to actually be.
Gender reassignment may be a protected characteristic, but it is still nonsense, and even though it is nonsense, it only covers men who want to be women and women who want to be men, not people who want to be cats.