I saw a documentary about this a few years ago, and, hearing the people who have BIID talk about it, I was struck by the similarities to transsexualism.
Just to correct something in a previous post, none of these people wanted to remove their arms, only their legs.
The strongest similarity was that legless was the way they were supposed to be, and that not being that way was an affliction that tormented them day and night.
The second strongest similarity was their frustration with a medical community that didn't understand them, didn't care about them, and set themselves up as the arbiter of something that should only concern the patient.
Watching the documentary, I was struck by the notion, as illogical as it might be - that both conditions could be explained by reincarnation, and the desire to be as we were in a previous life.