Edgar Allan Poe uses chronological events in "The Black Cat" in order to show the curve of transformation the narrator suffers through the story. At the beginning he used to like the cat very much, but after certain events that happen to him and that lead him to commit certain actions, he starts hating the cat.
Without the chronological events, the story would be very difficult to understand and we wouldn't be able to understand his internal motives to do something like that to the animal he used to love.
