There is a little to how good I could get at math, no matter how hard I tried. Maybe I should map out my argumentative flow chart a little better. Mental illness by definition cannot be a condition chosen at the moment at which it is occurring. But it isn't choosable at the moment at which I am suffering from it. I think imposing the same restriction on our concept of mental illness makes sense.
Some conditions considered to be mental illness are straightforwardly brain diseases.
E.g. Alzheimer's disease, and some effects of syphillis. I accept these without a problem. So the interesting class are mental illnesses which don't appear to be brain diseases. Now to begin with, it isn't clear that this idea is even coherent. Let's suppose that it is coherent.