Sir, that is not quite correct. It is not necessarily a sign of mental illness to get destructive/negative thoughts and emotions that lead to suicidal ideation.
We had extensive (and eye watering) education on the difference between a personality disorder and mental illness, and life changing events whenever a service member would off himself (which was far too common, thanks) over the two decades that I was a serving officer.
Unless you define mental illness as "not normal, like me"
Not normal and suicidal are not the same thing.
Not normal doesn't mean mental illness, of course.
But suicide is a serious mental malfunction, thus I might ask you what do you mean by "illness", if it is different ?