Here's a breakdown of the narrator's motivations:
* Obsessive Fixation: The narrator is consumed by the old man's eye, describing it as "a filmy white, with a pale blue around it," and seeing it as a symbol of evil.
* Desire for Control: The narrator feels powerless against the perceived threat of the eye, and killing the old man is his way of regaining control.
* Psychological Instability: The narrator's obsession and the way he plans and carries out the murder reveal his unstable mental state. He believes he is rational and sane, but his actions and the guilt that consumes him prove otherwise.
In short, the narrator doesn't simply want to kill the old man; he wants to rid himself of the torment caused by his obsession with the "vulture eye."