I think that the examples given regarding Self Delete can be taken in a scale, really.
I might wish I didn't exist for the day, solely so I don't have to put up with my responsibilities or any feelings of pain I might have, but it's definitely not sincere when I think about it.
I know that I don't want to die. My sense of self-preservation is definitely stronger than my desire to not exist.
The 'insane' obviously go a step further, where they go beyond entertaining the thought to sincerely contemplating it, and eventually acting out on it.
I suppose that is insanity.
And as an outside person looking at other people, we can never tell what is going on in someone elses brain. How far along that line of thought they are.
We only really know if someone confides the thoughts in us (in a sincere way) or if they do act them out.
We can't hope to read everyone's minds about how they feel. Insanity, in it's various guises, is often a silent disease.