In "The Cask of Amontillado," Montresor never gives a specific reason as to why he wants revenge. Rather, all that he tells us is that he had some personal slight against Fortunato. He claims that Fortunato had wronged him, grievously in his own mind.
Furthermore, if we are to believe his own words, it is certainly implied that this grievance had grown over time. Consider the very first sentence which opens the story: Montresor tells us, "the thousand injuries of Fortunato I had borne as best I could, but when he ventured upon insult, I vowed revenge." This unstated "insult" which he claims Fortunato had visited upon him, whatever it might have been, seems like it was more than anything else, a final straw, pushing him past his breaking point. Whatever ill will he held against Fortunato, it held much deeper roots reaching back in time.
That's all we can really say with any certainty.