I read that Reddit exchange with the doctor at the time.
She couldn't actually define gender, only in relation to expression and identity. She called other people bigots. She was utterly convinced that what she was doing was right, despite admitting that the long-term use of puberty blockers was untested.
It's like a self fulfilling prophecy. You halt puberty, so the person never develops the critical thinking necessary to question it, then go on to cross sex hormones.
I've heard many times that medical treatment is the only thing that works, and therapy is not effective. But firstly I haven't heard of any funding, research or studies on any kind of scale. In fact it appears to be discouraged. And secondly, it's suggested that the onset of puberty, although dreaded, can actually reconcile the person to their sex.
Maybe it's something to do with the brain developing at the same time, or the fact that puberty is nowhere near as horrendous as they first thought.