Children also learn very early that saying that they hate someone quickly pushes buttons, especially with parents. Encourage the mom to respond with something like, "I understand that you don't like what I did, but I still love you."
It sounds like the child you write about is taking this to the extreme. Suggest that the mom talk with the teacher to see what he or she has observed in the classroom. She could also talk with the school counselor and ask the counselor to spend some time with the girl.
This may be a phase that's over soon. But if these behaviors continue for a long period of time, the mom may want to consider therapy for her daughter. The school counselor or their pediatrician can help refer her to a therapist in the community.