When analyzing Montresor's attitude or motivation, readers must keep in mind that he is another one of Poe's unreliable narrators. So, Montresor's attitude is not necessarily what Poe considers moral or logical.
Revenge (or delivering "punishment") is the main theme of the story. Montresor states at the beginning of the story,
‘‘The thousand injuries of Fortunato I had borne as best I could; but when he ventured upon insult, I vowed revenge.’’
Readers never discover what those injuries are that Fortunato enacted upon the narrator, but Montresor does not portray that as important. This demonstrates that Montresor's attitude toward revenge is inarguable--he believes so strongly in his right to revenge that he does not need to provide specifics about his motive.
Moreover, Montresor believes that he is qualified not only to obtain revenge himself (and not wait on a higher power or give his enemy an opportunity for redemption), but he also demonstrates that he is entitled to choose the mode and extremity of punishment. Whatever Fortunato did to Montresor (if anything at all) obviously did not kill or physically harm the narrator, but he does not care about the punishment fitting the "crime"--he wants only to assert his power and sense of justice.