I think also that the idea of suicide brings sharply into focus the reality of how alone we are in the world (notwithstanding those who arn't ultimately alone!)
There is nothing whatsoever I can do to stop [the hypothetical] you killing yourself. And you cannot prevent me either. There is utter disconnect. Yes, we can use coercion, force, persuasion, but that only serves to highlight the fact that we are separate and that the only recourse we have is to such activities in which one separate 'body' is acting upon another.
The sense of aloneness brought up by the idea of suicide is also effect when we see that person thinking about killing themselves and we say: well I'm not coming with you. All the empathy and emotional connections that were/are supposed to be there are exposed by the idea of suicide as smoke and mirrors, when it comes to the crunch.