It's really a question of where mental disorders end and physical disorders begin.
In a sense, all mental disorders are also physical disorders because they're caused by physical differences in the brain, so really it's more a matter of if the condition can be "cured" through therapy or drugs (as with depression) and whether or not the condition is or isn't psychological along the same lines as other mental illnesses.
Maybe both forms exist, psychologically and neurophysically induced GID. I for one feel pretty sure from my own experiences and the various studies that have been done and examples like John Money's fantastically tragic efforts in discrediting his own theory, that brain sex does exist and can be in-congruent with the body. Likewise it's also not unheard of for people to feel they have GID only to later realize they don't, there's a lawsuit here in Australia against a gender clinic on grounds that they were misdiagnosed and now have genuine GID resulting from transition when their issues were related to something else.
Why should GID be removed? For one, there's increasing evidence that transexuality is literally a case of intersex brain structures. Not enough to prove it outright, but definitely enough to warrant consideration. If that turned out to be the case, then many, perhaps most examples of GID may in fact be subtle intersex conditions in the brain not causing any more noticeably mental illness. If that's the case, then those forms of GID would not be mental illnesses in the sense that there's nothing actually "wrong" with the mind itself.
I have very mixed feelings about the psychiatric profession, the more I learn about it the more I feel it exhibits an extreme amount of unscientific guess work, and that they really don't know much more about the underlying cause of mental or apparently mental disorders than the people who suffer from them would.
I for one would like to see GID removed from the DSM if for no other reason than its presence there assumes that it is a mental disorder when as time goes on more and more evidence is found that contradicts that assumption.
That and I don't like psychiatrists.

The primary problem here is, is GID a physical problem in the brain that can't be cured by conventional therapy, or is it a psychological problem that can be "cured". If it's the former, it's a birth defect and warrants just as much treatment as any intersex birth defect. If it's the latter, then it might be better if the psychological problem can be corrected, so the person can live a normal life without expensive surgical options.
I for one believe that it can be and frequently is a result of the former, in which case I don't think it should be listed in the DSM, or at least not as the same context as the latter possibility.
Its listing in the DSM has basically defined everyone with GID being as being assumed to be the latter category, and that it is the only category that exists. I think this is unhelpful to our situation and believe that in time it will come to be more widely recognized as a physical birth defect.
Homosexuality used to be considered a mental illness too, now it's widely believed it is simply a physical difference in the brain that is in no way a disorder of the mind, that's what I would like to see with GID.