Why does the narrator say that he killed his neighbor from the telltale heart?

In Edgar Allan Poe's "The Tell-Tale Heart," the narrator insists he killed his neighbor because he was driven to madness by the old man's "vulture-like" eye, which he found intolerable. He claims that the act was not born of hatred but rather a desperate need to rid himself of the eye that haunted him. The narrator's obsession culminates in the murder, which he believes will free him from his torment. However, his guilt ultimately manifests in the form of the imagined sound of the old man's heart, leading to his confession.