The narrator wants his audience to believe that he is not mad, seemingly as some sort of defense against his actions. Interestingly, he presumes that his audience has already determined his lack of sanity:

How, then, am I mad?

There is an implication in this line that he stands accused of madness, and this story is an attempt to clarify a misunderstanding of his character. He may be nervous—"very, very dreadfully nervous"—but he insists that this is not madness. He points to the fact that he can "calmly" tell the entire story of the way he murdered an old man—a crime committed for no reason other than the appearance of one of the old man's eyes.

The narrator explains that in his constant, dreadful state of nervousness, his sense of hearing has become especially acute. This is an important detail because in the end, the narrator claims that after his murder of the old man, he could still hear the man's heart beating. On some level, the narrator has an understanding that this is impossible; after all, he had dismembered the man and placed the pieces underneath the floor. Yet he clings to the belief that his perception is possible because of the heightened senses he has gained through his chronic nervousness, ignoring the reality that it is impossible to hear the heartbeat of a dead and dismembered man.

The narrator wants to build credibility and understanding through classifying himself as nervous instead of mad.