i) In the vast majority of cases, from what I've read, gender dysphoria is purely psychological. There may be rare instances in which it has a neurological basis.
One question is whether there's a reliable diagnostic technique to determine which is which. If a patient's condition is psychological in origin, it would be foolhardy to undergo irreversible surgery.
Likewise, puberty is an unrepeatable stage in the human lifecycle. If hormone blockers postpone that for too long, I assume the damage is irreparable. That's a lost opportunity. Unless you know for a fact that your condition has a neurological basis, why would you cross a line of no return?
ii) But suppose we can identify those for whom gender dysphoria has a neurological basis. In rare cases like that, is a sex-change operation the solution?
Medical science is a wonderful gift to humanity, but it's not a panacea. Medical intervention can't make you happy. There are many young, strong, normal, healthy, handsome men and women who are miserable. Medical science can't give you a happy life. You must have something worthwhile to live for.
iii) In addition, there are problems with medical science can't fix. It has many basic limitations. Even if your condition has a neurological basis, that doesn't mean its treatable or curable.
Take otherkin. Suppose, for the sake of argument, that lycanthropy has a neurological basis. Does that mean a lycanthrope should undergo extreme makeover surgery? Will making his body resemble lupine anatomy solve the problem? No.
He's not a wolf–even if he thinks he's a wolf. He's not a wolf–even if his brain tells him he's a wolf. He has no idea what it's like to be a wolf. He can't. He never will.
Pandering to his mental illness is not a cure–or even therapy. That's not treatment–that's mistreatment. He self-delusion is already self-destructive. Radical makeover surgery only treats symptoms, effects–and not the underlying cause.
The only way to cure him is to solve the problem at the source. Repair the brain damage. Stimulate new neural pathways. But, of course, neuroscience lacks the ability do to that as of now.
Not everything in this life is fixable. But this life is not all there is. The ultimate solution lies in the afterlife. Christian salvation. Heaven. The world to come.