"You are making a decision that they will have to live with the rest of their lives"
I hate this one. Especially under not too uncommon circumstances it can also backfire horrifically. To share some personal experience, you can get to this point from isolation, neglect, loneliness. At that point the feeling of being alone and having nothing important to you can take its toll really fast. A such described distraught and hurt individual could very well hear it as : "You're still not important, I care about the people around you." , "Don't do it: for the sake of the people that didn't help you", etc. and other variations. It's not particularly fair or reasonable, but it's entirely expected to not quite be in a fully rational frame of mind. Not only is trying to guilt a broken person a low tactic, there's so many reasons why it might not work. If the person has a bad history with friends or family, or just perceives that they never did anything to help them in their lives, there's a sense of being disinclined to care about secondary problems that group suffers.
If the person's reeling from tragedy or stress, sure it's a good idea. If they've just led a ****ty life and are tired of it, it'll only piss them off. And if you've just met the person you're not going to be able to tell the difference. Why go for the coin flip?
Make a connection with the person by talking to them. Say that you'll miss them. Especially if you're a stranger, the surprise from that might slow them down. Trying to reach out to the victim by highlighting other people sure is an odd way of convincing someone they're not unimportant.
Humans will inescapably see things from their view. However, sometimes we try and step out of that and put ourselves into someone else's shoes without realizing we're still wearing ours. If you're not thinking enough from the other person's perspective and are still considering the effects it'll have on you or other people... you're still not really stepping into that person's shoes. You have to realize that at the very least, in that person's mind they have a very good reason for being there. None of your own conceptions of what a person should be able to endure, what makes life living/meaningful, what responsibilities a person has, none of this will necessarily mean them same thing to them. They've got a problem that needs to be resolved. It's unlikely that you can do it on the spot, but you want to be sure you don't attempt to devalue that problem, it'll just push them away.
[/rant]. It's a pet peeve of mine, along with people that go around saying people that commit suicide are weak, which thankfully no one's uttered here yet.
(slight edits to grammar made)