The narrator believes that the second cat is the reason he's captured, but the readers know this isn't true what's the real reason the narrator was caught and convicted

The fact that the narrator gets caught is an example of his distorted view of reality.  From the opening line the narrator tells the reader that he has a "wild" story to tell, but that it is completely true.  He proceeds to tell the story of a cat who haunts him even after the cat is killed, so in his mind it's a ghost story.  However, the story is somewhat ambiguous because the narrator admits that he began drinking heavily, and so one might reach the conclusion that the alcohol has affected his view of reality.  Towards the end of the story the narrator is walking down the steps of the basement and the cat runs between his legs.  This angers the narrator, and he picks up an axe to kill the cat (for the second time!) but is stopped by his wife.  In his anger, he kills his wife with the axe and buries her in the wall.  The cat disappears after the narrator nearly killed him, and he believes the cat was too scared to come back.  The police come to investigate the wife's disappearance, and the narrator is so pleased with how well he hid his wife that he even takes the police to the basement.  In an arrogant gesture, the narrator bangs on the wall to show the police how strong and well-built the house is.  Once he does this, he hears a loud wail from within the wall.  As it turned out, the narrator accidentally buried the cat inside the wall when he was sealing his wife in the wall.  In the end, his distorted view of reality and his overconfidence is the reason why he is caught.  

yup its an addiction