Fortunato is annoying, but he definitely does not deserve to die.
Montresor’s argument for killing Fortunato is that he did him a thousand injuries. Yet there is absolutely no evidence that he did anything to him. If Fortunato had really done something to Montresor, I doubt he would have gone into the catacombs with him. He would have been expecting revenge.
What Fortunato is guilty of is being arrogant. Arrogance probably resulted in him snubbing Montresor or doing some little insult to him that hurt his feelings. This is what Montresor took to the extreme and decided he needed to die for, because Montresor is mad.
We know that Fortunato is arrogant because he wanted to look at the wine as soon as Montresor said that he was going to have someone else look at it. Fortunato believed no one else knew as much about wine was he did.
“As you are engaged, I am on my way to Luchesi. If any one has a critical turn it is he. He will tell me—”
“Luchesi cannot tell Amontillado from Sherry.”
“And yet some fools will have it that his taste is a match for your own.”
Even though he keeps coughing because of the “nitre” in the crypt, he insists on continuing. He wants to see that wine. Of course, it is carnival, and he is a little drunk. Still, it shows arrogance.
Another example is his reaction to Montresor claiming to be a Mason.
“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.”
He insists of proof (which Montresor does not have). Of course, Montresor is not a Mason. He is just trying to make a joke to explain the trowel. However, Fortunato’s insistence that Montresor cannot possibly be one of the members of this secret society of old families is another example of his arrogance.
Nonetheless, none of these things excuse what Montresor does. Fortunato is gullible and what happens to him is just sad. The man is remarkably dense and single-minded, but after all, he is drunk. Montresor took advantage of the day and the fact that he know Fortunato’s arrogance to get him down into the catacombs and kill him.
There is nothing in this story that makes the reader particularly hate Fortunato or justifies Montresor's murder. The reader may feel pity for Fortunator, because he is killed for no reason. He is the victim of a madman, who killed him because of some imagined insult. The reader may look for a reason that Fortunato should die, but such a reader may want to be looking inside himself.