The narrator's repeated assurances to the reader that he is sane reminds me of the Shakespeare quote regarding "... thou dost protest too much, methinks." Why would a sane man have to constantly defend his sanity unless he already suspects that he might be descending into madness? His reasoning is jumbled: He claims that the owner of the house has never hurt him, yet he decides he must kill the innocent old man. It is the old man's evil eye, the narrator claims, that forces him into killing him. He admits that he is "very dreadfully nervous" for no other apparent reason than the old man's eye. And he admits to a disease that "sharpens" his mind. Perhaps it is not the old man's eye, but
... the narrator really wishes to destroy the "I," that is, himself... by destroying the old man's eye, the narrator indirectly destroys himself in the end by exposing himself as the murderer. (eNotes, "The Tell-Tale Heart," Themes and Characters)
Little of the narrator's reasoning is sound. He makes detailed preparations for the murder and practices for days, but when the hour comes, his "foresight" fails to quietly subdue the old man. The solitary scream that is heard by a neighbor seals his fate. In addition to being a madman, our storyteller is also an unreliable narrator, one whose words must always be called into question.