If a kid has a heart condition and they have to have a risky surgery, the doctors ask the parents. Because the child is not old enough to understand the implications of these things.
I see gender dysphoria as a similar thing. The suicide rate is very high for these individuals so some form of treatment is essential if you care about your child. It's the same as if they had a heart issue with like a 40% risk of dying. It's life or death.
The transitioning process works best if it happens before puberty. When a child goes through puberty, the sexual hormones start pumping and that permanently changes many parts of the body. Literally the shape and size of bones will change.
If you catch gender dysphoria before puberty, the end result of the transition will be much more effective than doing it at 18 or 20. By that point there's no going back from puberty.
So essentially - the child isn't making a decision. The parents are making an informed medical decision based on a diagnosis by a medical professional.
I really don't see this as any different than any other medical issue. The difference is this is unusual and many people think emotionally.