What reason does the monster give for killing William and framing Justine in Mary Shelley's Frankenstein?
In Mary Shelley's novel, Frankenstein, the creature kills Frankenstein's youngest brother William, and frames another member of their household: Justine.
When the creature sits with Frankenstein and tells his story, he relates his trip to Geneva, coming by chance across young William. The creature believes that a child not having learned to be fearful of the world, might be a good companion for him. He tells William he will take the boy who will not see his family again, but the boy shares his identity as a Frankenstein, threatening the creature with his father's protection. Once the creature realizes this boy is related to Victor he says:
Frankenstein! you belong to my enemy—to him towards whom I have sworn eternal revenge; you shall be my first victim.
In order to punish Victor, the creature kills his young brother. In doing so, he discovers and takes the miniature portrait of his mother (Caroline) that the boy carries, away with him. Soon he comes upon Justine, asleep in the barn. She is not as beautiful as the woman in the portrait, but even as he thinks this, he knows that should she awake, she would reject him in horror as others had done.
Thus she would assuredly [denounce me if she] beheld me. The thought was madness; it stirred the fiend within me—not I, but she, shall suffer; the murder I have committed because I am forever robbed of all that she could give me, she shall atone. The crime had its source in her: be hers the punishment!
Knowing something of the law from listening to Felix, the monster plants the portrait in the folds of Justine's dress so she will be accused of the murder of William.
In essence, the creature kills William because he is related to Victor, and he frames Justine with the sense of power he realizes he has to bring havoc to the world around him: especially to her because she represents all he cannot have.