what differentiates these people from those who say they were born with the wrong genitalia? In both cases there is evidence to the contrary of the person's claims (no one is watching the paranoid person, a person's genitals exist as they exist). Why do we accept a transgendered person as being reasonable but a paranoid person as not?
A delusionally paranoid person would make a claim: "There are dozens of people following me with the goal to ruin my life". Their perception isn't possible to reconcile with the objective reality of "No one is following you, and no one just whispered 'Now you see how it works' into your ear."
In the first case, the person isn't delusional about objective facts, but their subjective interpretation is unusual. In the second case, the person and an outside observer would disagree about things that you'd expect to be objective facts. If the first person told you "No, that's not a penis", then the two people would be equally unreasonable.
The difference is that it's difficult to apply objective reason to subjective experience.
If someone abducted me and forced a sex-change operation on me, then I'd have to say that I had a vagina, but I'd still say that I was a man. I'd consider the physical state of my body a result of an act of mutilation.
Them saying "I am a woman", or me saying "I am a man", is a statement of gender (a social construct) rather than sex (a biological fact).
Traditionally, we'd consider sex and gender to be in lockstep, and it wouldn't be useful to consider them as anything but perfect synonyms. "I'm male" is a simple enough concept. It means three things: that I have a penis, consider myself male, and I'm attracted to females.
Add in the 5%-ish of the population where the 3rd point is completely false, and the larger percent where it's true, but not completely exclusive.
Add in the smaller segment of the population where the second point doesn't match the first.
Add in the yet smaller segment where even the first point doesn't have a binary truth value.
This isn't to say that there aren't delusional people that would argue about the observable biological state, just that mostly I'd think they're talking about their perception of their own gender, rather than their perception of their sex.
Reminded me of "The Skin I'm in"
Transitioning as a solution to gender dysphoria works. It drastically increases the quality of life of those who suffer from it. Sure, in an ideal world where we had full knowledge of human biology and an ability to edit the brain, we'd treat gender dysphoria simply by making people believe they were the "correct" gender. But lacking that ability, we do the next best thing possible that we can do.
On the other hand, you can't cure paranoid schizophrenics in any sort of similar way.
There is [a small propaganda war being waged by transphobic conservatives][] to create the illusion of a large percentage of trans people that regret their transition, but just look at their references. You'll find every link is either to the Daily Mail or some other hate group referencing even more hate groups in a big web of circular reasoning.
Generally, there's not a lot of hard data to work with on issues relating to the trans community right now, which is a little frustrating, but hopefully there will be more soon as the scientific community is finally starting to recognize the LGBT community and conduct real science on this stuff.
[1]: https://www.reddit.com/r/asktransgender/search?q=regret&rest... [2]: http://www.sexchangeregret.com/
The identify of the person is the mind; the being that thinks.
If the body is not a match for the mind, then the correct solution is to repair the body.
Why are you more keen to edit the brain than the body? If I can switch around your body parts to make you feel more comfortable, that seems less invasive than surgery or drugs which make you think different thoughts - especially when those thoughts are a core part of your personality (your sexual identity) and are only pathological within the context of the body you were born with.
But just because someone has a specific mind now doesn't mean that they'd want to change it. There are lots of people who want to change their minds. I suspect that most people with depression and other mental disorders would love to have the option to get a treatment that changed their mind to remove that condition. I bet most of us here would change our minds in order to be smarter, and indeed some people are already taking drugs that claim to be able to do so (though the entire field is in its infancy). More to the point, at least one transgender person I know says she wishes she could've simply changed her mind to agree with her body rather than go through the entire process of changing her body. Our minds are maybe more malleable than you think.
So first off, what if you applied the same question to sexuality? We could easily argue that gay people are 'mentally ill' and need to be 'treated.' In fact, for years in the United States, that's exactly what we did. Gay people (and trans people) were frequently [subjected to electro-shock therapy to 'cure' them][]. We can even take it further than that. If I come by my political beliefs by reason, then surely anyone who disagrees with me politically must therefore be insane. So maybe we should give those damned INSERT_POLITICAL_PARTY_HERE electro-shock too, right? Just until they see our way of looking at things.
Clearly, there's a line somewhere between treating someone's disease and treating _who they are_. Some argue that that line is 'posing a danger to oneself or others,' but that brings up the confusing subject of assisted suicide, which is a whole other discussion. There's also some that argue that we only treat 'abnormality' and 'normal' is simply whatever the majority of people are, but that doesn't really solve either of the cases above, because trans people, gay people, and political dissidents are generally speaking the minority everywhere. There's also lots of other possible rules that don't really makes sense either.
Personally, I'm inclined to believe that there currently aren't any good answers to these questions and there won't be any until the field neuroscience advances. When we can look at people's brains and genuinely study how they work, a lot of stuff becomes more clear. In the case of transsexuality, [some brain structures have already been identified][] that exhibit one pattern in women and another in men and tend to match along a person's _identified_ gender rather their _assigned_ gender. That provides some evidence for the concept of _neurological sex_ which was already a topic of discussion among researchers in the area of gender studies even before these structures were identified.
So, what do these structures mean? How does gender work in the brain? How does anything work in the brain? Where is the line between sane and insane? Honestly, I don't know, but I think we'll have a better idea in a few decades, and until then, let's just try to be understanding and compassionate with our fellow human beings.
[1]: https://www.amazon.com/Whipping-Girl-Transsexual-Scapegoatin... [2]: http://www.huffingtonpost.com/jamie-scot/shock-the-gay-away-... [3]: https://en.wikipedia.org/wiki/Causes_of_transsexualism#Brain...