A Primer On The Three Main Situations Where "Go Kill Yourself" Is Used On The Internet:
1. p1: "I am so depressed, I wanna die"
_ p2: "Do it! Do it!"
This person is a tool. They are profoundly incapable of empathy over the internet, and should ideally have their internet access revoked.
Level: Complete *******ry, always inappropriate
2. p1: "Something really stupid"
_ p2: "You are stupid. Go kill yourself."
This person is insensitive; often they are attempting to make a joke, but by bringing suicide in a completely inappropriate/irrelevant context, they demonstrate that they do not really comprehend the potential impact of those words.
Level:In poor taste, though the issue is primarily one of escalation (aka jumping from normal conversational levels to suicide jokes without making sure everyone ends up on the same page)
3. p1: "If xyz, I would kill myself" (hyperbole)
_ p2: "XYZ!! So...does that mean you're gonna do it?"
This person is taking a preexisting lighthearted reference to suicide and calling the bluff. It is primarily a way to highlight the ridiculousness of the initial statement in an attempt to elicit laughter and/or get the OP to recognize the overintensity of their sentiment.
Level: Mostly harmless, often quite amusing. Done in good spirit, though as with any joke, there are situations where it can be taken too far.