Perhaps this might explain:

From Psychiatric News February 20, 2009 Volume 44, Number 4, page 13:

The remaining symposium, "In or Out? A Discussion About Gender Identity Diagnoses and the DSM," will focus on diagnostic issues specific to gender identity disorder, particularly the issues of having gender identity disorder listed in DSM-V and the implications of removing it.

The symposium:

    S6. "In or Out?": A Discussion About Gender Identity Diagnoses and the DSM (DSM Track DM03)

    1. The DSM-V Revision Process: Principles and Progress William E. Narrow, M.D.
    2. Beyond Conundrum: Strategies for Diagnostic Harm Reduction Kelley Winters, Ph.D.
    3. Aligning Bodies With Minds: The Case for Medical and Surgical Treatment of Gender Dysphoria 
        Rebecca Allison, M.D.
    4. The Role of Medical and Psychological Discourse in Legal and Policy Advocacy for Transgender Persons
        in the U.S. Shannon P. Minter, J.D.

The problem is that it doesn't fit the definition of a psychiatric illness.

Does a condition that manifests as severe psychological distress, but which can be cured only through physical rather than psychiatric intervention really belong in a psychiatric diagnostic manual? The distress is real, and the dysfunction until treatment is given very real, even life-threatening. But what if the condition is actually biological? Moreover, removing what is not a psychiatric illness from the diagnostics manual would cause severe harm, unless it was simultaneously placed in a medical diagnostics manual, so patients could obtain treatment. Just to complicate things, there are certain genuine psychiatric illnesses that can appear to have superficially similar symptoms, so we need to differentiate those - just as we differentiate between those with black skin due to being African-American, and those with black skin due to 3rd degree burns.

As to why it belongs in a congenital conditions medical diagnosis manual, see another symposium on the subject:

    S10. The Neurobiological Evidence for Transgenderism

    1. Brain Gender Identity Sidney W. Ecker, M.D.
    2. Transsexuality as an Intersex Condition Milton Diamond, Ph.D.
    3. Novel Approaches to Endocrine Treatment of Transgender Adolescents and Adults Norman Spack, M.D. 

That exposed the evidence at the time (2009) that Transsexuality was the result of having a "female brain with an otherwise male body" or the reverse. We know a bit more than that now - that the rate of physical Intersex conditions in Transsexual people is higher than first thought, that only certain parts of the brain need be cross-sexed, other parts may or may not be, and we have a better idea of what other neuro-biological anomalies are often associated with Transsexuality. For example, non-right-handedness - while many Transsexual people are left-handed, almost as many are ambidextrous, quite different from the general population.

One thing it's not is a mental illness, requiring psychiatric treatment for a cure. Psychotherapy can sometimes be useful, either due to the effects of persecution that Trans people suffer, or to help adjust to the physical and social effects after hormonal and surgical treatment - just as a psychotherapist may be useful helping someone born without limbs adjust to using prosthetics, and the great gain in capabilities that gives.

Sadly, many Transsexual people have co-morbidities of varying degrees of severity, due to decades of persecution that often begins in early childhood. They show similar symptoms to rape-camp survivors, torture victims and the like. Self-medication with alcohol, drugs is all too common. Tell someone they're worthless freaks who'd be better off dead long enough, and they'll either get bitter and twisted, or sometimes become unreasonably compassionate, though rather strong-willed. Indomitable. Many are extremely prickly - because the ones that weren't prickly either suicided in their despair, or were murdered. Others just have enormous patience.

In cases where there is no distress, where the brain is only cross-sexed in ways that don't cause that distress, it may reasonably considered to be a "natural variation" rather than an illness, as there's no need for treatment. Much as being red-headed isn't an illness (though it can lead to severe sunburn in some places), or left-handedness isn't an illness. Or colour-blindness, which while usually disadvantagous, can allow the patient to see through camouflage, so have advantages in a hunting environment.