Hm … good question. I don’t know. I also don’t care that much … let me explain.
I don’t think transsexualism is a mental illness – after all, it seems that exactly the same processes and mechanisms shape gender identity in both transsexuals and non-transsexuals. In addition, transsexualism seems to be unrelated to mental illnesses. (Some evidence is provided here: What is transsexualism?, What causes transsexualism? and Summary.)
Physical sex characteristics, such as the genitals, are also developed normally.
The issue with transsexualism is that physical sex and gender identity don’t match. Both are normally developed, but are not aligned with each other, they mismatch. This mismatch causes gender dysphoria. It’s intriguing that a healthy mind and a healthy body can produce such an effect. Medical classification and categorisation is made more difficult by this exceptional situation.
Nonetheless, the transsexual has a condition which can reduce quality of life quite drastically and can cause afflictions such as depression and anxiety. This condition can be improved upon or even cured with some medical and social interventions.
Now it comes down to semantics … the definitions of words. The Oxford dictionary says illness is “a disease or period of sickness affecting the body or mind”. Disease is a “a disorder of structure or function in a human, animal, or plant, especially one that produces specific symptoms or that affects a specific location and is not simply a direct result of physical injury”. Lastly, a disorder is “an illness that disrupts normal physical or mental functions”. Hm, leaving aside the circular definitions of illness → disease → disorder → illness, does transsexualism fit into this category? Maybe, maybe not.
As someone suffering from gender dysphoria, my mental functions are okay, but I do have a feeling of uneasiness or discomfort which can be debilitating. So it would probably not be entirely correct to say that my mental state is completely undisturbed and regular. Thinking it around the other way, if I’m absolutely fine, why do I feel miserable and need help?
So transsexualism might fall under the Oxford dictionary definition – or not, depending on whether one thinks that mental functions of gender dysphoria sufferers are disrupted (“interrupt an event, activity, or process by causing a disturbance or problem”) or not.
For comparison, Wiktionary says for illness: “an instance of a disease or poor health”. Disease is defined as “an abnormal condition of the body or mind that causes discomfort or dysfunction; distinct from injury insofar as the latter is usually instantaneously acquired” and a disorder is “a physical or psychical malfunction”. So, let’s see what criteria gender dysphoria meets… illness/disease: discomfort or dysfunction, yes – abnormal condition, yes – of the body or mind, hmm, no. Same for disorder – gender dysphoria is not a physical or psychical malfunction, the problem arises from the mismatch between both.
Looking at Wiktionary, gender dysphoria doesn’t seem to fit the definition of illness.
I think these two examples illustrate the problem. It is largely a semantic problem, an issue of word definitions. Due to the exceptional nature of transsexualism, it is hard to find the right categories and abstractions.
As a layperson, without thinking through all the details, my personal understanding of illness has been something like: “A condition of the body and/or mind which reduces quality of life significantly compared to the norm.” With this understanding, gender dysphoria is an illness. Also, transsexuals usually require medical treatment (hormones and surgery), which should be covered by health insurance. Why should get transsexuals access to medical treatment and insurance coverage if they are not ill? Seems illogical to me. Or should we perhaps create a new category, of people who are not ill, yet require medical treatment? Seems complicated.
So, that’s my opinion – transsexualism is neither a psychological nor a physical illness, but I’m usually okay with it being called an illness. Sorry it’s so confusing. ☹
Well… if that’s confusing… it can still get a lot more complex, if you throw value judgements into the mix. Some people believe that the words “illness”, “sickness” or “disease” carry negative connotations, reflecting badly on an individual. In this view, transsexuals are discriminated against and stigmatised when called “ill”. Same for the word “disorder”. It might imply that there is an “order”, which is the culturally sanctioned norm, and deviations from that norm are wrong, false, and negative, i.e. have a lesser value.
Transsexualism of course, is a natural phenomenon that doesn’t come with any intrinsic value judgements. There is also no reason why the feelings, wishes, emotions and life of a transsexual person should have lesser value than those of a non-transsexual person. Transsexuals are not delusional, cognitive functions are not impaired. Everybody is equal, has the same worth and deserves the same respect and dignity. Growing up transsexual isn’t of lower value than growing up non-transsexual. Naturally, this has to be reflected in our language, anything else wold be discrimination.
However, gender dysphoria is “bad” in the sense that it reduces quality of life and is a risk factor for serious illnesses. Transsexuals recognise this when they try ease their dysphoria by medical and other interventions. And this is one major difference to homosexuality. Homosexuals do not require any medical or other intervention. Homosexuality doesn’t cause a reduction in the quality of life – quality of life is only reduced indirectly through discrimination by society. This discrimination we have to eliminate!
But even if there was no social, cultural or religious discrimination whatsoever: Fact is, gender dysphoria can be debilitating, and it often requires medical treatment to improve.
I’m probably not smart enough to consider all details of the argument… but, as you notice, I don’t think the label “illness” for gender dysphoria is discriminating or pejorative for transsexuals.
Maybe there is one thing to add: Reflective people know anyway that it is wrong to reduce individuals to one aspect of their persona. Same is true for transsexuals, of course. Yes, a transsexual person is a transsexual, but that doesn’t say anything about personality, character, sexual orientation, or other aspects of our identity. The value and individuality of the person are completely unrelated to the label “transsexual”.
Anyway, that is my take on it. Being ill does not and should not carry a stigma. Maybe it’s of help that the English languages offers terms such “medical condition”, which might seem unaffected by questions of political correctness (however, when trying to define it in comparison to illness, it gets hairy).
So, being called transsexual, suffering from gender dysphoria, does not imply any value judgement, it is simply an objective statement of fact. Gender dysphoria itself is a “bad” thing as it reduces quality of life, but that doesn’t suggest anything about the affected individual.
 An existing exception might be pregnancy and birth. However, pregnancy requires medical treatment only when something goes wrong.
 I find this view offensive. It is victimising and demeaning to assume that people who are ill might be thought less of, or that being sick somehow reduces the worth of an individual. The illness itself is “bad”, yes, but obviously that does not imply any criticism or assessment of the affected individual. However, the label “ill” becomes a problem when it is inappropriately used to take agency away from the person (“that’s just your illness talking”).
 Political correctness notwithstanding,I think it should be possible to call people redheads, blondes, Italians, heroes, actresses, thieves, Buddhists, swimmers, conscripts, cheats, liars, doctors, lesbians, nerds, school children, geniuses, addicts, taxi drivers, cancer patients, etc. … and, yes, also transsexuals or transgenders. It should be obvious to anybody with half a mind that such a description illustrates only one attribute of many that a person has. Naturally, this kind of abstraction should be used only when relevant to the context, not to denigrate a person. A friend of mine said something very smart when she remarked: “It is my experience that people who cannot make the distinction between using abstractions and actually thinking in abstractions are the ones who generalise more.” It took me a long time to understand what she meant, but now I think she has it spot on. And anyway, why should the term “woman” or “transsexual woman” be better or more politically correct than just “transsexual”? The first one reduces me to my gender, the second one reduces me to two aspects, my gender and my transsexualism. That still doesn’t give a rounded view of who I am, and my gender might not even be relevant in the context. So, no, I don’t have big issues with being a “transsexual”, since I expect it to be universally understood that such a single label doesn’t define me.
 Sorry about the length of footnote 3!