If a man puts on a dress, he's still a man underneath. Allowing a man, pretending to be a woman, so he can go in women's locker rooms and compete against women is against nature, nature's God and science.
GK Chesterton said it best, "Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who merely happen to be walking about...Tradition asks us not to neglect a good man's opinion, even if he is our father."