At the story's beginning, the narrator insists that he is not mad, and he presents himself as a victim. Indeed, he tells us that he will die on the following day, and he says that he is telling us this story simply to "unburthen [his] soul." As we hear his story, however, it becomes increasingly clear that he is actually quite mad, or at least has been, and that he is not a victim but rather a cruel psychopath.
Early in the story, the narrator tells us that, one night, after drinking too much and becoming "intoxicated," he decided to cut out one of his pet cat's eyes. He offers no better reason for this act of cruelty than being drunk. A little later in his story, the narrator tells us that he soon after decided to kill the same cat by hanging it from its neck. He says that he killed the cat "in cool blood."
The spirit of this cat haunts the narrator for the rest of the story. First it appears as an image, an "apparition" on a wall, and then it seems to be reborn in the body of a second cat. In the form of this second cat, the spirit of the first sets about tormenting the narrator, reminding him of his guilt, and eventually the narrator becomes quite mad.
Perhaps the epitome of the narrator's madness is when he kills his wife. His wife tries to stop him from striking at the second cat with an axe, and in response, the narrator flies "into a rage more than demoniacal" and buries the axe in her skull. The narrator then buries the body of his wife behind a brick wall. When the police come to search his house and, initially, fail to discover the wife's body, the narrator says that he felt a "glee at [his] heart ... too strong to be restrained." This feeling of "glee" indicates that the narrator's behavior is not only cruel and mad but also psychopathic.