Not sure I'm quite up to such a discussion but...
I am one who does not like to use the term "mental illness." I, if necessary, will say mental unwellness.
However, if I were to say that mental illness doesn't exist would not mean that suffering mentally doesn't exist. It's when people hear the term "mental illness" that most (somewhat ignorant?) people assume it is a problem caused by someone's emotional reactions/imbalanced thinking or such. I do think as we continue to learn, that we will find that the mental aspect of the illness one might suffer from is just that, a mental display of a symptom or symptoms, but that the cause is hardly emotional, but physical. Whether it's hormones, or brain chemistry misfiring or another type of cause that's truly physical, doesn't take away that people still suffer from real illnesses.
I fully think that even those disorders that find CBT helps them heal show that we can re-change those brain chemicals back to a good balance for living, and not that we "happen" to be feeling bad only because we are thinking poorly. (But, in further explanation, the poor thinking causes the changes in the brain chemistry over time...)
So, let me say again, no matter what someone calls it, or doesn't, in my mind it doesn't mean the real life suffering doesn't exist.