I've definitely thought myself round in circles lots of times on this one!

When we say 'illness' we most often mean 'affliction' or 'infirmity', 'poor health' or 'sickness,' so I suppose... I suppose whether ->-bleeped-<- is a 'mental illness' or not entirely depends upon how it precisely affects the individual. If you feel afflicted or debilitated by it, then it's an illness for you.
In its essence, I guess, it's a characteristic. One person might be proud or delighted or indifferent to a physical or mental characteristic that is a source of pain, discomfort or distress for another.
It undoubtedly places significant life obstacles in the path of anyone transgender - largely due to the physical and emotional upheaval created by dysphoria, which is in turn in great part due to society's (thankfully *gradually* lessening) discomfort with gender 'transgression'.
And there's a particular stigma attached to the phrase 'mental illness' that does and perhaps should discourage us from labeling ->-bleeped-<- as such. Then again, there's the argument that there should be no stigma attached to the phrase 'mental illness.' I'm in two minds on this one... I suffer from extreme OCD - a characteristic, like ->-bleeped-<-, that places numerous challenges in my path and does often distress and trouble me... and I feel no shame or reluctance to label that as a 'mental illness.' Then again, my impulse to repeatedly, compulsively and ritualistically repeat actions in response to obsessional thoughts debilitates me completely negatively and unproductively, whereas my ->-bleeped-<- has the potential to be an extremely positive force - there are aspects of it to do with self-realisation, self-expression, bravery, exploration and personal fulfillment that elevate it, for me, far above the category of 'mental illness.'
I know there are varying and opposed medical theories and opinions on the causes and nature of transsexualism. But just on a human level, I feel that its nature is fluid and can depend enormously upon the individual and their own attitude towards it (which, in turn, can depend upon many factors, including the individual's environmental circumstances).
To categorically call it an 'illness,' though, is undoubtedly wrong, because this only becomes a self-fulfilling prophecy. If it's viewed universally as an illness, then those with the characteristic will see it as such, those around them - their families, their friends and their doctors - will see it as such, generate unhappiness, obstacles and unpleasantness and it will become nothing but an illness and a trauma.
Hopefully, at some point in the future, society will be so accepting that there will be no trauma or difficulty when someone realises that their mind and their body are differently gendered - we'll just say, when we realise it, 'I'm transsexual,' and it'll be like discovering you're a Maths genius, or want to be an astronaut, or can roll your tongue or wiggle your ears. It'll still throw up some challenges - the necessity for hormone therapy and surgery to align body and mind - but these will be nearly painless (mentally), as people will view them to be as obviously logical and necessary as sending a Maths genius to a school for the gifted. That's the way it should be. It'll happen, eventually, I like to think.