Harry just wanted to thank Narcissa for saving his life; he never expected to or meant to become penpals with her, become friends, even. Narcissa only thought Harry was a sweet boy, and felt a strange motherly instinct toward him. She felt terrible that he even thought he had to thank her for what she did for him. When Harry starts having relationship troubles, her motherly instincts come out, and so do the claws. Narcissa is utterly and solely kind to Harry, but Draco? Not so much.