There's a huge difference besides the fact that transgender isn't called a mental disorder anymore, I'm not sure you guys are updated with that. people that are pedophiles are almost always abused as kids and transgenders can have a normal life until they're 70. You're not a pedophile as a kid and I know this sounds silly but my point is that theres always a reason they end up there as adults, some studies even suggested lower iq, abuse as mentioned, seeing obscure things as a kid, being unrecognized by the other gender while having a mental disorder. Psychopaths are a prime example of people who can have a normal live or they can be serial killers without remorse.
Transgender people are just feeling unlucky they're born the wrong way. If you think logically it's not that strange considering we're humans and rather than using instincts we think, we decide what we want to do, and we do it.
There was a time being gay was a disease and science established that wasn't the case, now most transgenders are gay and there's probably some correlation there. If you want to believe they're born with a more feminine gene fine I can buy that but to say that pedophiles are like transgenders is at absolute best redicilous.
If you get kicked by your mother your whole childhood you might end up hating women, being born a psychopath might make you kill them without any remorse. Being raped by your dad won't turn you gay but it might turn you in to a pedophile, having your mom dress you like a girl wont turn you in to a transgender.
NOT THE SAME