Poe has Montresor address his confidential communication to a single individual whom he calls "You, who so well know the nature of my soul." This is a brilliant literary device and foreshadows Ernest Hemingway's "iceberg theory," which also involved leaving out exposition. In doing this, Poe relieves himself of the need for providing a whole lot of exposition and can focus on the actual crime, the dramatic action, itself. Poe does not even have to mention where the events took place. Some readers actually think the crime might have occurred in New Orleans! Or perhaps in Kansas City, Missouri? Poe does not have to describe the "thousand injuries of Fortunato" because, presumably, he has told this confidant, or confidante, all about his relations with Fortunato before, presumably in letters.
I believe it is a mistake to assume that Montresor wants revenge because of some unspecified "insult." In my opinion it is the "thousand injuries" for which he wants his revenge. The insult, whatever it was, only shows that Fortunato was becoming more obnoxious and insufferable, and would continue to infuriate Montresor in the future.
Why does Montresor put up with a thousand injuries? Why does he associate with Fortunato at all? There is no need for Montresor to explain this to "You, who so well know the nature of my soul," but we readers have to play Sherlock Holmes and deduce from the existing evidence. Here is the third paragraph of the story in full:
He had a weak point—this Fortunato—although in other regards he was a man to be respected and even feared. He prided himself on his connoisseur-ship in wine. Few Italians have the true virtuoso spirit. For the most part their enthusiasm is adopted to suit the time and opportunity, to practise imposture upon the British and Austrian millionaires. In painting and gemmary, Fortunato, like his countrymen, was a quack, but 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.
This suggests that Montresor and Fortunato deal in luxury items. They are not Italian noblemen but gentlemen-brokers and connoisseurs. Fortunato is rich. Montresor is poor. Montresor may depend on him for loans, finder's fees, ad hoc partnerships in single transactions, and other such financial benefits. Fortunato may have cheated Montresor many times or taken unfair advantage of him in other ways. Since these matters would be between the two men, Montresor could continue to speak of Fortunato as "my friend," "my old friend," "my good friend," and "my best friend," in order to convince everyone, including Fortunato himself, that they were good friends and thereby forestall incurring any possible suspicion when Fortunato turns up missing. Montresor has so thoroughly conditioned himself to thinking of Fortunato as his friend that he refers to him constantly as such throughout the story, even when he is taking him to the niche where he intends to chain him to the granite wall and leave him to die of starvation and madness.
Fortunato will not die for a single insult but for a thousand past injuries.