Considering that hormone treatments, sex change operations etc. are pretty recent inventions I think that explains it.
Transgender people have been a part of many societies throughout history such as:
In India:
http://en.wikipedia.org/wiki/Hijra_(South_Asia)
About the eunuchs in India of which there are an estimated 2 million today.
Native Americans:
http://en.wikipedia.org/wiki/Winkte
I had always heard they were called Berdache but apparently that term is no longer preferred.
It's actually fascinating to read into the variety of forms of gender expression found throughout human history. They extend far beyond that accepted in the West- which is, traditionally, unusually narrow-minded in regards to both sexuality and gender expression- and encompass a surprising range of expression, limited not just to m-to-f or f-to-m gender transition, but a variety of genderqueer, polygender and gender fluid identities as well. In some cases, they are even attributed a spiritual value and so greater social status- as in many indigenous American cultures, where bigendered people act as shamans and other spiritual leaders- challenging the idea that gender transgession represents any self-evidently "wrongness" in human society.
One thing that seems to be a recurring feature in traditions of trans womanhood or feminine third genders is that they allow an expression of same-sex attraction for men in cultures which do not accept homosexuality or bisexuality, but do not proscribe same-sex intercourse
per se. (It seems to echo, to some extent, a recurring perception in many cultures that only the bottoming partner in male same-sex intercourse is emasculated, as they are taking on the "feminine" role of being penetrated, while the topping role is essentially the same as in opposite-sex intercourse.) I've heard it suggested that it acts as a sort of semi-conscious alliance between non-heterosexual men and trans women (and other male bodied feminine trans people) in conservative cultures which allows them both a greater expression of their sexuality and gender identity.
No, they would probably feel a crippling disassociation with themselves if they did, to the extent that the dissassociation that goes with being Transgendered is 'crippling.'
I think that you either over-estimate the depth of conviction felt by child amateur kickboxers, under-estimate the depth of conviction felt by trans people, or live in a parallel universe in which Ong Bak is actually true.
I would like to hear your thoughts on the comparison with Body Integrity Identity Disorder and Otherkin.
Well, I'm given to understand that studies of transsexual neurobiology- as mentioned by El_Machinae earlier- are suggesting that transsexual people are, in fact, a form of intersex person, possessing mental architecture similar to that of the opposite sex, which, for whatever reason, leads their brain to expect a body which is not there. This could lead to a mental condition similar to BIID, I suppose- I do not pretend for a second to know much about the details!

- but if it does indeed have objective biological origins, rather than the primarily or purely psychological ones which I am given to understand are associated with BIID, it seems that the proper thing to do is treat the mis-matched body as the problem, rather than the mind.
As for Otherkin... Well, if I understand properly, the Otherkin, as well as those furries with a more literal understanding of the "fursona" (of which I believe the Otherkin are essentially a breakaway current?) don't believe themselves to be animals, mythical creatures, etc. in quite the same literal and immediate sense that transsexual people believe themselves to be a sex other than which they were born (especially given the aforementioned neurobiological issues),but to have the spiritual or otherwise immaterial "essence" of the creature in question; that they do not have the same disassociation with their physical body, but, rather, see it as a sort of material host. My pet theory is that it reflects some innate resonance that shamanic or totemtic practices have with humans, expressed in clumsy and sometimes ill-considered ways. Having a slightly tree huggish side to me that I don't exhibit here very much, I will admit to being relatively open-minded about such things, although I must admit that the particular practices of the people in question often strike me as somewhat self indulgent.
