I like your thinking!
When I was in school learning hypnotherapy, we briefly studied gender identity. I think we were using Version V, and now I think we are on to version VI.
There are different classifications for various mental issues. "Dysphoria" merely means being somehow disturbed by something. I have "Neighbor Dysphoria" because my neighbors disturb me often. However, it is not classified as a "disorder" unless it interferes with your life (socializing, family, work, school, etc.). So you can have Body Dysphoria, meaning you are disturbed by how your body looks, acts, or is shaped. Many people who are transgender may not be "disturbed" by it enough to want hormones or surgery. They are no less transgender, they just are not dysphoric to the point of it being a disorder. Their coping mechanisms allow them to live in stealth or be content with the uneasiness.
Back in earlier versions of the DSM, this distinction was clear and it was called "Gender Identity Disorder". This is what we now call "Gender Dysphoria". But note that it is not a "disorder" unless it is severe enough to interfere with one's life. Now they have everything lumped together under the diagnosis of "Transvestism" with two sub-categories. One for cross-dressers and one for transgendered persons.
Another thing concerning the "mental illness" part. The reason is to determine if one is dysphoric, and is that dysphoria a disorder. It is also to determine if some other cause results in that behavior or thinking. One could be schizophrenic or delusional. Gender Identity is mental. You can't see it on an MRI, so it must be examined by a mental health professional. The point is to narrow it down to a specific diagnosis. You can go to a physician and not be sick. Most mental health professionals go to other mental health professionals. It doesn't mean they have a mental illness.
My psychologist's diagnosis is something along the lines of "Transvestism: with chronic gender dysphoria since adolescence." He didn't know me when I was young, so he made that determination by my answers to his questions and the descriptions I gave when relating specific events. In my opinion, it started when I was about six years old, but his diagnosis accomplished the same thing. For many of us, puberty is the most difficult to deal with (if we have a disorder).
