What does Montresor admit is the motive for his crime in "The Cask of Amontillado"?
Montresor states that the motive for his crime is revenge. In his mind, he is the long-suffering innocent party who has suffered "the thousand injuries" of Fortunato with forbearance, but when "insult" follows, can endure Fortunato no longer. For Montresor, revenge is not a simple matter, but must be carefully executed: to succeed he has to get away with his crime without being caught, and his victim must know that Montresor is the agent of his doom.
Poe writes in the Gothic genre, characterized by gloomy, un-homelike (unheimlich) settings, psychological terror, and such uncanny features as death and doubling. This leads us to wonder if Montresor might subconsciously perceive Fortunato as his double or twin (doppleganger), a reading supported when Montresor explains that "in the matter of old wines he was sincere. In this respect I did not differ from him materially; —I was skilful in the Italian vintages myself, and bought largely whenever I could." If this is the case, is Montresor's real motive an attempt to "bury" parts of himself he abhors and can't face by killing his double? Is "revenge" simply a rationalization?
In Edgar Allan Poe's short story The Cask of Amontillado, the narrator, Montresor, has been the apparent target of a lengthy series of probably subtle but pointed insults at the hands of Fortunato. I say "subtle" because the intended victim of Montresor's wrath has no inkling that Montresor considers him an enemy. Montresor, though, has been enduring a string of indignities that has clearly left him in a vengeful mood. The suggestion of cumulative insults is offered in the story's first sentence:
"THE thousand injuries of Fortunato I had borne as I best could; but when he ventured upon insult, I vowed revenge."
At no point in Poe's story does the author provide any further clues as to the nature of grievance. It is sufficient that the atmosphere has been established through this simple introduction. The precise nature of the insult is immaterial; this is a story about a man determined to avenge his honor, and who most certainly succeeds, albeit in a way that only he will ever be able to fully appreciate.
Montresor commits the crime against Fortunato because he perceives he has been insulted. We never find out what the insult is, but it doesn't matter if you subscribe to the idea that "perception is reality". Whether or not there was an insult, Montresor was insulted.
Revenge is really the motivation. Montresor has blown the insult issue out of proportion and is determined to seek revenge in order to right the situation and save his honor. He is obsessed with revenge and has certainly gone to great lengths to exact it.
The only thing Montresor tells us is that Fortunato insulted him, but we never learn what Fortunato supposedly did. Since Montresor is the narrator, he isn't very reliable, so it's possible that Fortunato did nothing to Montresor. The offense could be in Montresor's mind only. His family motto is no one does anything to a Montresor without the offended Montresor taking revenge. So it's a family tradition in the Montresor family to avenge any and all perceived offenses.