In many cases at 10-12 years old. We normally wouldn't trust a 10-12 yo to decide diddly-squat. Imagine arguing 10 yo is old enough to decide to have sex, for example.
AGAIN, NOT SAYING I think this way, but that's underlying 'argument' these people are making. They're tender babes, they haven't developed enough to decide, they may change their feeling about it if they go through puberty matching their biological sex, etc.
I have to admit though that PRIOR to being educated by others, esp. here on DU over the past few years, I might've given that argument some credence, but it wouldn't have been out of trans-phobic views, at all.
Very unlike the assholes at the forefront of the CON side, who ALSO want to keep kids from drag-queen story hour, refuse to allow kids to even be educated about the phenomenon, don't want trans people to use the bathrooms they feel are proper, etc. That shit absolutely gives away what it's really all about for them. The kid-angle is mostly a front for their bigotry.
Thru being educated, I've come to understand that the major medical organizations support this kind of treatment, that there are considerable and thoughtful medical protocols that are followed in all cases, and that very very few people ever decide to transition back or later feel that they wish they hadn't been allowed to go through with the choices they made with their parents when they were young.
So what you say is the key point, and it helped advance gay rights considerably in the past. This is who they are, it's not a 'choice', and not a 'fad'.