I'd say it might be more accurate to say that no one wants to have gender dysphoria, just like no one wants to have any sort of medical condition. Being transgender though... well, for me it helps to think of being transgender as the cure, not the illness so to speak. Being able to transition is what is allowing me to move forward in my life after years of living in a world of anxiety and depression--something that applies to many of us here. Maybe if he tried to think of it in that light, it would help?
And remind him, no matter what else, he is light years ahead of most of us by dealing with this at his age. Let him know he should be proud of that, proud of facing this now and not 16 years down the line (me at 35) or more. God knows I wish I had the same courage he does to address any of this when I was still a teenager.