What is the man vs. man conflict of the short story "The Cask of Amontillado"?
It's Montressor (the narrator and protagonist) vs. Fortunato (the victim and antagonist).
The problem is...we don't know what Fortunato has done, if anything, to initiate the conflict. Montressor says that he has born a "thousand injuries." The reader, therefore, must deduce that, since Fortunato so willingly goes into the catacombs with Montressor and does not pick up on all the signs of his impending doom, that the "thousand injuries" must have been either invented or so trivial that an otherwise sane person would have not taken offense to them.
This is a revenge story, similar to the one in Othello between Iago and Othello. There too we do not know the reason Iago seeks revenge on his lord. So, in each story, the motive is questionable. It may be that Iago and Montressor are simply vice characters: they represent what Coleridge called a "motiveless malignancy." These narrators are pure evil to the core, but they are so charming about it so as not to breed suspicion.
It is also evident that Montressor comes from an honor culture, one that prides itself on family and personal repuation. Fortunato might have been from a family that had done the Montressors wrong in the past, and only now is the narrator seeking revenge.
The man vs. man conflict in this story is that of our protagonist and narrator, Montressor, behaving in conflict with his victim, Fortunato.
Fortunato's fate is first foreshadowed for the reader by his somewhat ironic name, which contains the root word "fortune." We do not know until the end of the story that this "fortune" is not a positive one, but rather, his own death, the most absolute and negative fate of all.
The story itself is one centered upon the idea of avenging past perceived wrongs, as Montressor is bent upon murdering Fortunato for the "thousand injuries" that Montressor alleges Fortunato has carried out upon him. We as readers are left to infer what those injuries may be, and to determine how severe or slight they actually were.