What is ironic, or deliberately contrary to what the Fortunato expects, about Montresor's concern for his health is that Montresor's real intent is to cause harm to the man.
Another interesting aspect is that Montresor's verbal irony has not only the intent of deceiving Fortunato that he is worried about his cough, but it also has a subversive motive behind it, as well. For, in addition to feigning concern for Fortunato, Montresor repeats the opposite of what he means in order to spur Fortunato to move farther and farther into the catacombs more recklessly and irrationally. Evidently, Montresor has discovered what Mark Twain calls "a great law of human action; namely,
...that in order to make a man or a boy covet a thing, it is only necessary to make the thing difficult to attain. [The Adventures of Tom Sawyer]
Thus, with the ironic concern and urging for them to turn back, Montresor makes "the thing (the Amontillado) difficult to attain," so that Fortunato covets it all the more, and in his cupidity loses his reason to the point that when Montresor fetters him to a wall, Fortunato is "too much astounded to resist."