You want I to be outdated, so you choose to accept all evidence that makes you feel good and reject all evidence that makes you feel bad.
Serious question here: if you met a homeless man suffering from pschizophrenia who believed he was Jesus Christ resurrected, would you be oppressing him by telling him that all the evidence points to him not being Jesus? Would you be out of line if you told him, compassionately, that he needed help? Aren't those who enable his delusions, and tell him he really is Jesus, doing more harm than good?
It isn't comparable at all. A transgender feels like the gender of his or her body, doesn't match the gender identity he or she feels. So you might be born in the body of a female while you feel you are male, or the other way around. (I am sure Sammie can explain this much better than I can.) It doesn't have anything to do with sexuality. A transgender can be hetero, bi, or gay.
I also find it hard to fully understand, but I also think that's just because my body is female and I feel female too. These 2 things (body and identity) are linked for me, and that feels so normal, 'like it should be', that it's hard to imagine that some people feel like that physical gender doesn't match with who they feel they are. Maybe the difficulty we have with truly understanding shows how linked the body and the mind should be? And how natural it is that these people want a body that represents their identity?
You can't, by the way, compare being hetero, bi or gay with being a pedophile either. Although being a pedophile might also not be a choice, the big difference is that relationships between consenting adults (in whatever which combination possible) are between equals, while pedophiles are attracted to children, who can't consent and which causes the relationship always to be un-equal by nature. I'm not stating ALL pedophiles engage in relationships with children (luckily that's not the case), but the lack of equality does make pedophilia incomparable to other sexual orientations. And that, I think, is precisely why pedophilia is listed as a mental disorder and also why being compared to a pedophile offends almost everyone.