Why does the narrator of "The Tell-Tale Heart" believe he will not get caught for killing the old man?

The narrator believes he will not get caught because he thinks that he's pulled off the perfect crime and that his capacity for dissimulation is greater than everyone else's.

After he has killed the old man, he says, "If still you think me mad, you will no longer when I describe the wise precautions I took for the concealment of the body."  The first thing he does is to dismember the corpse so that it...

The narrator believes he will not get caught because he thinks that he's pulled off the perfect crime and that his capacity for dissimulation is greater than everyone else's.

After he has killed the old man, he says, "If still you think me mad, you will no longer when I describe the wise precautions I took for the concealment of the body."  The first thing he does is to dismember the corpse so that it is easier to hide. He seems especially proud of the fact that he thought to do this dismembering in a "tub [that] had caught all" so "There was nothing to wash out, no stain of any kind."  He pulls up three floor boards and buries all the old man's body parts underneath them.  The narrator believes that he did such an exact and careful job of replacing the boards that "no human eye [...] could have detected anything wrong."  His arrogance is extreme; we can see that he certainly believes himself to be more intelligent and deceptive than any other person has the capacity to be. 

Even when he hears a knocking at the door, he "went down to open it with a light heart -- for," as he says, "what had I now to fear?"  Now that he's ridden himself of the old man's vulture eye, he believes he has nothing left to concern him.  He lets in the police officers who have come to investigate the cry his neighbors heard when he killed the old man, repeating the line, "for what had I to fear?"  He is convinced that "The officers were satisfied.  [His] manner had convinced them."  The narrator's immense pride in his ability to behave calmly and to think intelligently, makes him believe that there is no possible reason he cannot get away with this crime.