"The Tell-Heart" is a murder mystery, the kind where we know who the killer is (sort of), but can't really understand his motives. This story deals with the fear of death, with dying, and the question of how a person can kill another. As such, Edgar Allan Poe's story is suffused with an underlying sadness, and a sense of mourning.
Because the narrator believes that the old man is a vulture, he thinks he's killing the old man in self-defense.