Why does Robert Ross’ mother tell him to kill the rabbits, and what might be the larger significance/symbolism of this act?

His mother wants the rabbits killed because she feels they were responsible for his sister's death (she died in a fall from her wheelchair while playing with her rabbits). Robert tried to stop their killing and was beaten for it. The significance of this is the fact that his mother wanted him to carry the guilt of his sister's death.

Robert's decision to not kill the rabbits also forshadows his stron connection to animals.