To answer your question OP, the reason why the “biology” argument is a touchy subject is that it is usually used as a dog whistle by transphobes. Rowling is very sly in the way she words these things, in the way she wrote her weird twitter essay especially. Framing it like she’s fighting for feminism, she looking out for the poor cis women and their safe spaces. Whilst at the same time, framing trans women as not real women and potential threats, and trans men as these poor women who become men because they can’t handle the patriarchy. I’m not making this shit up, read her blog.
She says that if we allow trans women to use women’s public loos then the rate of assaults will go up. Despite the fact that trans women use women’s loos anyway, that trans women are more likely to be on the receiving end of violence and that cis man can walk into these public bathrooms anyway. Nothings stopping them. They’re not waiting to slip on a wig and a dress to assault women. She also says that trans men are “misguided” women. Trapped by the patriarchy so they seek an escape by becoming men…. okay. Whatever you say, Rowling. She says shit like this and claims to be the victim whenever someone disagrees with her. Oh yeah, and she likes and shares statements from known TERFs. I was a huge Harry Potter fan.