While i certainly don’t think you should allow your daughter to transition at such a young age, you should consider the possibility that she legitimately transsexual and suffers body dysphoria. If she does, only then should she transition. But I am completely 100% in agreement with you on how stupid these new definitions of gender identity are.
But what causes body dysphoria? Before transgender became a popular, hip thing, there were a relatively small number of people who were so unhappy in their bodies that they chose a sex change operation. No one was celebrating and pushing them in subReddits and on YouTube and Tumblr. All of these young lesbians who suddenly become keen on “transitioning” seem to acquire the idea that they are dysphoric from watching OTHER lesbians who claim to be dysphoric on YouTube magically changing into straight boys high on testosterone. I think this especially happens with shy, socially awkward teens who spend most of their time on the web, and who are having trouble with forming strong relationships in real life. Not to mention that the latest push is to make it even easier to change genders. In transactivist circles, it’s considered oppressive to have to wait at all, to have to get a letter, to spend time “living as a man.” The trans movement thinks even young teens should be able to get immediate access to hormones and surgery as soon as they want it. They decry the “gatekeepers” who won’t just let them start transitioning NOW.