Guess I'll die meme
In this particular instance of the meme, the the person decides that dying is preferable to calling someone. There are a lot of people that don't like calling people, so many people can sympathize with the feelings presented in the meme. That makes it funny in a sort of self-deprecating way.
Here is another instance of the meme:
In this one the person is giving up on life because no-one seems to care if they live or die. It is a bit dark, however if that were all that it took to make someone despair of life, it is sort of funny. The magnitude of the reaction is not commensurate with the magnitude of the trigger.