If we understood bleeding as poorly as we understood cancer, then everything from R&D for better bandages to public campaigns to reduce gun violence would be lumped together as "treatment for bleeding."
There are many types of cancer just like there are many types of bacterial infection. But they are both well identified. We can see the cancer cells and bacteria, and when they are gone, the patient is cured.
Mental illnesses are more like the "flu-like syndrome". The causes can range from leukemia to heroin withdrawal to a wide variety of viral infections like AIDS, the common cold, and of course, the flu. You can treat the symptoms with Tylenol but we can't really call that a disease, more like the symptoms of a yet undiscovered disease.
Also, once it's there, we know it's there, and we know exactly how to cure it: destroy all the cancer cells. The hard part is doing it without killing you in the process, and making sure that not a single cell is left in the end.
Just because we don't know now, doesn't mean we will never know. That's how science works.
People have 'mental illness' because of mental problems, not physical problems.
Also: everything has some genetic component, this is trivially true. Genetics are what separates humans from dogs and plants. It doesn't necessarily help us to explain the phenomenon adequately.
Also also: another way science works is its inability to prove negatives. Therefore, saying, "someday we might discover this" can be said for pretty much anything that remains unproven.
If your identical twin has schizophrenia, there is a 48% chance that you will have it too. This is compared to the chance of the general population, which is something like 1%. This feels like something is physically wrong in those who are schizophrenic. I don't know how else you would get that kind of result.