In fairness, I was hasty in dismissing the 'growing' one considering that in some cases, as in fact I'd already mentioned elsewhere in this discussion, doctors will indeed try to intervene in the growth process, however natural it may be, when it looks like the child is going to be abnormally tall. Can't think of any reason why one might want to prevent teething - though, as I also mentioned already, we can and do regularly fix people's entirely naturally grown teeth. Including, by the way, through surgeries to remove entirely healthy wisdom teeth.
Society as a whole and, I assume, you yourself have no issue with people getting medical treatment for things that are quite natural, even when in the strictly physical sense there is no disease and no treatment is absolutely required - because people's health is about more than just the strictly physical sense. For many of such things, as with gender reassignment surgery, medical science now gives people far more and better options in such cases, when their ancestors would've had to just deal with it however they could. The only real limit is what medical science is capable of - the solutions offered may still be far from perfect, or may come with significant downsides, so decisions still need to be made case by case for each patient.
You have an issue with this particular form of treatment simply because you philosophically insist, firstly, that man and woman are fundamentally different and changing from one to the other is impossible on general principle, whatever medical science can or can't do, and secondly, that even the desire to make that change is irrational or even wrong - possibly because you believe in a Creator who had those people born into that particular body for a reason. That's really the crux of the matter, because if you philosophically accept that gender reassignment is something that can be done, albeit imperfectly and with downsides, and you consider the desire for it as unusual but rational enough (unlike for instance the Body Integrity Identity Disorder that entyti brought up, i.e. people fantasizing about having healthy body parts amputated), then gender dysphoria can be 'cured' simply by giving the patients what they want, so as 'mental illnesses' go, that's a remarkably simple one to fix. Doctors wouldn't 'give patients what they want' if what they want is objectively bad for them, like with BIID, but there's nothing objectively bad about a man becoming a woman or a woman becoming a man - provided, again, that you don't dogmatically deny the existence of that possibility.
I have zero expectation of making you change your mind on those philosophical points and I don't assume you have any expectation of converting me to your point of view, either, but hopefully it'll clear up some things.
Some genetic quirk such as being born into a body with the wrong genitals and hormones, perhaps? Sure, you don't think that such a thing exists - but yeah, see above, that's a matter of philosophical dogma.
The 'anathema' captures it better than the 'insane', since your failure to understand is a problem of dogma, not logic.
Skipping a few paragraphs because they retread the same ground as above. This doesn't - and wow, I find this position a lot harder to understand than your position on trans people, since that's just dogma I don't share, not sure what this is though. In my view, while there does need to be a legal age of maturity somewhere and 18 seems a reasonable one, people are mostly shaped by life experiences, not age as such, which means that there are plenty of 13 year olds in the world who in many ways are more mature than some 65 year olds. Not in all ways of course, the mental impact of puberty is still a thing, but whenever you put people into surroundings where their age is invisible or somehow socially irrelevant (including, of course, online forums such as this one and its predecessor), you see how relative age differences really are.
You didn't answer the question about what if the parents are on board with the puberty blockers and the gender transition more generally, as is often the case?
Certainly, I never thought you meant to encourage physical violence - though as I'm sure you're aware, trans people do encounter physical violence frighteningly often and even if you do fundamentally disagree not only with what they've done but even with the premise of that being possible at all, you could still show more respect in how you talk about them.
Both very true.
I already said why - because I wanted to see if your views on how much say a child should have in deciding about puberty blockers were similar to your views on how much say they should have in other difficult medical decisions.
As for 'mental anguish has nothing on physical suffering' - that's a pretty absurd thing to say. No doubt it's easy for you to dismiss the particular mental anguish of gender dysphoria, for the abovementioned philosophical reasons, but I'm still pretty baffled you'd believe that in general? Unless you mean it as some kind of motivational statement along the lines of 'sticks and stones may break my bones but words will never hurt me' - which you may find useful to tell yourself when you're feeling down, but absolute nonsense as a general factual statement.