People seek to draw a link between suicide and mental illness because the drastic outcome of suicide stretches one's comfort with the notion of informed consent.

The widespread societal taboo against suicide supposes that no rational person free of undue pressures would consent to ending their own life, therefore anyone who commits suicide must have been pushed to do so by serious factors that impaired their ability to properly consent.

This line of thinking effectively re-defines 'mental illness' to be that unknown variable that pushes outwardly functional people towards a choice that surprised the observer.