An interesting question. Does it have to be a single trait? If so, then it is monomania, as is the case for so many of Poe's characters. He has a single fixation (that cat!) which overwhelms all other aspects of his life.
If we're allowed to consider more, I'd say alcoholism, self-deception, and near madness. He drinks himself half blind, and manages to blame the cat for an anger that drove an ax into his wife's skull and killed her! He can then live with himself, and I'd say he can do so due to all of these traits combined.
Greg