Why do you think the narrator begins the story by telling us he is not mad?
The narrator of "The Tell-Tale Heart" by Edgar Allan Poe is, as we discover as we read through the narrative, clearly insane by our standards. He also has an obsession with convincing us of his sanity, and emphasizing his rationality and intelligence.
From the point of view of the narrator, the story is almost an argument proving that he is sane, by giving examples of he cleverness and planning. Thus he sets out his point, that he is not insane, at the beginning of the story and then tells a narrative with concrete examples that are intended to prove his sanity.
From the point of view of the reader, the way the narrator repeatedly insists that he is sane gives us our first clue that the narrator is, in fact, insane. People who are normal and sane by the standards of their cultures do not need to insist on their sanity.