The narrator of "The Black Cat" could be considered unreliable for a number of reasons. First, he tells us that he is not "mad," but he very well could be. This is a person who tells us that he tortured animals, including cutting the eye out of a once-beloved pet cat, and he actually hanged this cat by the neck until it died. Thus, the narrator might literally not be in his right mind, and this would make him unreliable.
Second, the narrator confesses to becoming an alcoholic, to succumbing to what he calls "the Fiend Intemperance." He suggests that his alcoholism made him violent toward his animals as well as, eventually, toward his wife. It caused him to "maltreat" his pets, even when they approached him seeking affection. He was often "intoxicated," and so it is possible that his memory of the events he reports is not accurate. This is another way in which he could be seen as unreliable.
Third, the narrator's character is clearly deeply flawed. He abuses animals and, eventually, murders his own wife because she sought to keep him from killing their pet cat. He kills her and expresses next to no remorse for the murder; in fact, he conveys his deep happiness that the cat seems to have disappeared. Such a person as this might seek to be deliberately deceptive, as we know that he manages to deceive the police officers who come to investigate him for the disappearance of his wife.