In the beginning of the story "The Tell-Tale Heart," what is the attitude of the narrator?

In the first paragraph of the story, the narrator is concerned to convince readers that he is not insane. He insists, for example, that his senses are sharp and acute. He says he was and is "dreadfully" nervous but also states that he can tell his story calmly. He questions why anybody would call him "mad."
While trying to communicate his sanity, the first-person narrator immediately raises in our minds the idea he is not sane. Why, we wonder, has he been accused of insanity? If he is very nervous, how can he tell his story calmly? How do acute senses, especially hearing, correlate with sanity? Can't you have acute senses and still be insane?
If the first paragraph raised doubts, the second paragraph even more strongly contradicts the narrator's assertion that he is sane. The narrator proceeds to tell us that he decided to murder the elderly man he lived with for no other reason than that he "had the eye of a vulture."
In the third paragraph, the narrator is still insisting he is not mad and pointing to his "caution" as a proof of his sanity. We, however, are looking at the fact he murdered a man for no logical reason.