I don't think it is supportive to tell someone feeling suicidal to not kill themselves, but neither is it supportive to tell them to do it.

Suicidal ideation is a symptom of a deeper issue... it is a coping mechanism. Telling someone to not kill themselves is not addressing the root cause... but a symptom. Even worse, it doesn't replace this coping mechanism with something else. 
You are basically telling someone in deep distress and pain to not do something that they believe will bring them some comfort, that will enable them to cope with the situation they are in. The focus becomes their symptom rather than on them and their inner turmoil.