Montresor’s motive for leaving Fortunado in the catacombs is revenge for Fortunado’s insults against him.
Although he never tells us exactly what Fortunado did to him, Montresor opens the story with charging Fortunado with a “thousand injuries.” Chances are these supposed insults were minor imaginings of a raving mind, because Montresor is not quite right in the head.
Montresor is obsessed with the perfect murder. He is convinced that he is not really getting revenge unless he gets away with it. If he is caught and punished, that will not really be sweet revenge.
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.
This is why Montresor chooses to brick Fortunado up in the catacombs, where no one will find him. He will suffocate and die there, and no one will ever know that Montresor killed him.
The irony is that Fortunado has no idea that Montresor is even angry at him, so he doesn’t suspect anything. There are no signs that he is going to his death.
The simple answer to the question of why Montresor wants to kill Fortunato is that Montresor hates him. It doesn't matter whether Montresor is sane or insane, or whether he is justified or unjustified. He hates Fortunato so passionately that he wants to kill him in a horrible manner. Also, he wants to be sure that he doesn't get caught and punished. This is certainly understandable without a lot of explanation. Nobody would want to commit a murder and get sent to prison or executed. Montresor feels that he has been injured and wants revenge. He works his murder plot out carefully and is completely successful in every respect. When he tells the entire story in confidence to someone he addresses as "You, who so well know the nature of my soul," fifty years have passed. So it is obvious that he has achieved a perfect crime and that he has received the "closure" which was his main objective. His hatred for Fortunato tormented him. Once he has achieved his revenge he is cleansed of his tormenting feelings. That is why people seek revenge. He no longer feels any hatred for his victim. That is why he closes with the words, "In pace requiescat!" He means this sincerely.
In "The Cask of Amontillado" Monstresor does not fully reveal why it is that he holds a grudge against Fortunato:
"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 gave utterance to a threat."
However, he does make it clear that his sole intention when leading Fortunato to the vault is to take his life or punish him for this in-explicitly stated wrong:
"At length I would be avenged; this was a point definitely, settled --but the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish but punish with impunity."
Perhaps the ironic usage of the word mason near the end of the narration is a clue to the offense that Fortunato has committed against Monstresor:
"I looked at him in surprise. He repeated the movement --a grotesque one.
"You do not comprehend?" he said.
"Not I," I replied.
"Then you are not of the brotherhood."
"You are not of the masons."
"Yes, yes," I said; "yes, yes."
"You? Impossible! A mason?"
"A mason," I replied.
"A sign," he said, "a sign."
"It is this," I answered, producing from beneath the folds of my roquelaire a trowel."
Monstresor mentions that Fortunato was a powerful and respected man, and that his only weakness was that related to his pride of his connoisseurship in wine. The emphasis on Fortunato's high social status, in combination with Monstresor's decision to kill him through masonry, could suggest that that Fortunato's offenses were related to our narrator's exclusion from this elite social group.