I think Anita is her mother and I think toward the end it became clear why Granny lied. Obviously Granny wanted Red to have a normal life, as much as possible. Anita wanted her to join her wolf clan and learn to hate humanity (she did try to eat Snow…). Granny is always protecting Red. I kinda love Granny.
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"He was a lot of things to me" "The only conclusion was love"