Why doesn't Montresor reveal the "insult" that prompted his revenge against Fortunato?

You are right. Montresor doesn't specify the insult he received from Fortunato. But he doesn't mention any of the thousand injuries either. Some critics have speculated that Montresor is insane and that he never received any injuries or insults from Fortunato. I personally believe that Poe wanted to make his story as short as possible, in accordance with his rationale that there should be no unnecessary word in a short story; and if he got into describing a lot of injuries it would add many words of exposition. Critics would still be free to doubt whether any of the injuries he cited were real or imaginary. If we can't take Montresor's word that he received a thousand injuries and at least one insult, then how can we take his word about anything in his story? Everything else he says seems sane enough to me. Isn't that a good way to judge his sanity?

I think Poe wanted the reader to gather some idea about the relationship between Fortunato and Montresor during the course of the story. Fortunato is not interested in the Amontillado because he wants to drink it or because he wants to show off his connoisseurship. Amontillado is a sipping sherry. If he drank a lot of it he would get sick. What interests him is that Montresor got a bargain on a whole cask of it. From what Montresor says early in his narrative, it appears that both he and Fortunato deal in art, jewelry, and probably wine--any expensive items that would appeal to millionaires. But Montresor is obviosly poor. If a ship from Spain brought in a cargo of Amontillado, Fortunato might be able to buy many casks at an even greater bargain price. Both men refer to the cask as a "pipe." A pipe of wine is 126 gallons. Fortunato, who is rich and well connected, has probably been able to beat Montresor out of many bargains in art works, jewelry, ceramics, tapestries, antiques, and wines over the years, and I presume these constitute the bulk of the "thousand injuries" Montresor has received. Why? Because how else could any man have inflicted so many injuries on another man if they weren't competitors? What is the difference between an injury and an insult?

Evidently the insult wouldn't have impelled Montresor to seek such terrible revenge if he hadn't suffered a thousand injuries before. The "insult," whatever it was, was the straw that broke the camel's back. Montresor's motivation is of the utmost importance, but does it matter whether or not it is justified?

Why doesn't Montresor reveal the "insult" that prompted his revenge against Fortunato?

This is a question which every single reader of "The Cask of Amontillado" must ask himself. Obviously, Edgar Allan Poe never gives us a specific reason, only that there had been "the thousand injuries of Fortunato," and that, at some point, Montresor's adversary had gone too far, forcing the narrator to take revenge. Perhaps Montresor (or Poe) chooses not to reveal the exact insults to maintain a mysterious aura; it could also be because Montresor is retelling the story 50 years in the future, and the reasons are either unimportant or long forgotten. Since Montresor's narration almost takes on a sense of confessional (perhaps to a priest or relative), his goal may be to only confess his own crime, and not Fortunato's.

Why does Montresor wait so long to reveal what he did to Fortunato?

Montresor does not tell everyone what he did to Fortunato. He very prudently refrains from telling anyone for fifty years, and then he is evidently only telling one person about the incident. I believe Poe intended to have his story understood as narrative written to a confidante in a letter. That letter would have been written in French or Italian, and most likely it would have been found among the friend's papers after that man's or woman's death. Then somehow or other it would have come into the hands of an American who was interested in old books and other old documents and curiosities, and that American, Poe, translated it into English and published it in an American magazine. It is also possible that Montresor wrote the confession in a letter one night while drunk and decided against mailing it when he became sober. In that case the manuscript would have been found among Montresor's papers after his death, and this could have been even more than fifty years after his commission of the murder. This, of course, is all part of Poe's fiction. It seems most likely that the fictitious Montresor would have written a narrative rather than telling the whole story aloud in a long monologue.

Why does Montresor wait so long to reveal what he did to Fortunato?

In "The Cask of Amontillado," there is a perverse pride that Montesor takes in his revenge and its methodology.  In fact, the motivation for Montesor's narrative is to relate how cleverly he has effected his exact and appropriate revenge upon Fortunato.  This first-person point of view is the lens of Montesor's irrational narrator whose main desire is to describe in minute detail his fulfillment of his family's motto: "Nemo me impune lacessit."

That Montesor tells his tale with the intention of instruction is apparent in his first paragraph as he states the lesson to be developed for his reader: 

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.

Then, in his conclusion, Montesor displays a pride in the success of his plan, the development of his lesson, as he declares that

For the half of a century no mortal has disturbed them.  In pace requiescat!

Thus, he has achieved his objective stated in the first paragraph.