What explanation does the monster give for killing victor brother?

The monster in Mary Shelley's *Frankenstein* does not kill Victor's brother, William. The monster strangles William as a way of getting revenge on Victor for creating him. The monster believes that Victor's abandonment of him and the suffering he endures as a consequence of his existence are all due to Victor's actions. William, being Victor's brother, becomes a symbol of Victor's family and happiness that the monster feels he is deprived of.

It's important to remember that the monster's reasoning is complex and driven by a sense of isolation, loneliness, and rage. While he initially intended to be kind and helpful, he is ostracized and rejected by society, leading to his descent into violence.