Over the course of the story, the source of Sylvia's antagonism shifts. Initially, Ms. Moore, with her "nappy hair and proper speech and no makeup" is hated by Sylvia and her friend, Sugar. They hate her, Sylvia says, the way that they "did the winos who cluttered up [their] parks." Ms. Moore enters their space in a way that they find disagreeable and against the norms of their community, due to her embrace of a natural hairstyle, her higher level of education, and her dismissal of traditional femininity. Furthermore, Ms. Moore is a dark-skinned black woman ("black as hell") with no shame around her appearance.
Like a lot of adolescents, regardless of background, the narrator thinks that she knows more than those both younger and older than she, assuming that her community and its rules are applicable everywhere. Her exposure to economic and racial inequality shift her focus away from Ms. Moore, specifically, and toward the circumstances to which she has exposed the children. However, Sylvia, unlike Sugar, is ill-equipped to articulate the real problems and cannot admit her powerlessness against the source, so she remains angry with Ms. Moore and races against Sugar, determined with the thought, "[N]obody gonna beat me at nuthin."
It would make less sense to tell the story from Ms. Moore's perspective because it would diminish the impact of the character's epiphany on the reader. Bambara sets up the world through Sylvia's eyes, which are limited by youth and class. A third-person omniscient narrator would interfere and know too much. This is, after all, a story about the things a young girl does not yet know about the world.