The narrator in Edgar Allan Poe's "The Black Cat" builds up to the moment he kills the cat for several reasons:
* To establish a descent into madness: The narrator's escalating cruelty towards the cat shows a gradual loss of control and a descent into a darker, more violent state of mind.
* To highlight the contrast between the narrator's initial affection for the cat and his later hatred: The initial tenderness serves to highlight the shocking and disturbing nature of his later actions.
* To create suspense and foreshadowing: The narrator's growing obsession with the cat builds tension and foreshadows the inevitable act of violence.
* To explore the nature of guilt and remorse: The buildup allows the narrator to detail his internal struggle with guilt after the act.
In essence, the buildup serves to create a psychological portrait of a man driven to madness by his own dark impulses. The act of killing the cat becomes a culmination of this descent.