One of the things Edgar Allan Poe is known for in his short stories is a unreliable narrator who wants us to believe that he is perfectly sane even as he reveals his most heinous acts with the utter belief that they are completely "normal" and justified.
Montresor is the narrator of "The Cask of Amontillado," and he is probably the least revelatory about the state of his sanity. What he does do is make it clear that the thing that prompted the act he is about to reveal was a horrible offense.
THE thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult, I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat.
As Poe's narrators usually do, Montresor assumes that we (the readers) know his soul and tacitly approve of the things he does.
The truth is that Montresor commits a horrible murder (walling Fortunato into a wall of an underground crypt) just because Fortunato somehow insulted him. The slights and insults could not have been significant, for Fortunato still speaks to and acts without malice toward Montresor. This narrator suffers form some form of mental illness or insanity.
In "The Black Cat," the narrator is writing his story to readers the night before he is going to die. Over and over again in his opening paragraph, the narrator expresses his belief that what happened to him (not what he did) was nothing more than a series of common and unremarkable event. He calls this a "homely narrative" about a "series of mere household events," "an ordinary succession of very natural causes and effects." The horrible things he does, including abusing animals and his wife before finally killing both, are not ordinary events which might have happened to anyone. Contrary to his insane belief, we do not approve.
Finally, the narrator in "The Tell-Tale Heart" also downplays his own madness as he reveals his actions to his readers. He admits he is nervous. It is true that his senses have been sharpened. He hears things "in the heaven and the earth," but of course that does not qualify as madness. And, of course, if he is calm he cannot be crazy, right?
True! --nervous --very, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses --not destroyed --not dulled them. Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad? Hearken! and observe how healthily --how calmly I can tell you the whole story.
The horrendous and senseless murder of an old man is certainly madness, but the narrator would not say it is so.
All three Poe narrators falsely assume that their readers will agree with them. All three of these Poe narrators are convinced that they are perfectly same because the things they do seem quite normal and natural to them. In fact, it is their view of horrible, murderous acts as normal which proves they are insane. They try to insinuate themselves with