According to Montresor, what is his motive for the crime he commits in "The Cask of Amontillado" by Edgar Allan Poe?
Unfortunately, there is not really a satisfying answer to the question of motive in "The Cask of Amontillado" by Edgar Allan Poe. There is an answer, it is simply not a good enough answer to justify what Montresor does to Fortunato. Montresor tries to explain his thinking in the opening lines of the story:
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. At length I would be avenged; this was a point definitively settled -- but the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish, but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.
What he wants us to believe is that Fortunato had somehow done him thousands of "injuries" which Montresor has managed to graciously overlook; then Fortunato insulted him and that was all Montresor could take. The insult must, of course, have been monumental to overshadow (be worse than) a thousand injuries, so when we read the rest of the story we are looking for signs that Fortunato really does bear some kind of venomous hatred toward Montresor.
Unfortunately for Montresor, we find nothing of the sort. Instead we watch Fortunato greet Montresor like an old friend, willingly follow Montressor to his house, and even joke with him in Montresor's underground crypt. It is true that Fortunato is full of pride and therefore falls into Montresor's cunning and well conceived trap; however, we find no evidence that Fortunato has any negative feelings against anyone but his rival, Luchesi. Montresor's claim to motive, that he could no longer bear the consistent insults by Fortunato, does not seem to be substantiated by the facts.
It is our nature to expect a heinous crime to be precipitated by a heinous grievance because then at least it makes sense. Without that, such a foul act seems monstrous and unprovoked, and it is the same kind of reaction we have to school shootings and other senseless acts of violence. Since we do not have a motive sufficient to explain the crime, we can only assume that Montresor is not sane, for a same person would never commit such an atrocious act.