The first person point of view is powerful in that it draws the reader into a more intimate understanding of the character. In "The Lesson" Sylvia, the narrator, comes to understand the hard lesson of economic inequality and exists in her inner city world. It is important that Sylvia, rather than Ms. Moore, be the narrator for this story for a couple of key reasons.
First, Sylvia is an apt narrator because she is a representative of her community and of the age group that the lesson is appropriate for. Ms. Moore, even though she is also African-American, is viewed more as an outsider because of the way she talks and dresses. Sylvia can provide the reader with more detailed knowledge of the other children as well. In this way, the reader comes to know the diverse group of children in their own environment and to understand the way they view the odd world of grown-ups. As a grown-up, Ms. Moore cannot provide this perspective.
Second, this story is about the realization, an experience that the reader gets to feel along with Sylvia. Unlike many of the other children, Sylvia comes to understand the lesson and is angry at the implications. In this way, the reader, too, can become angry and empathize with these children raised in poverty. Ms. Moore, who is teaching the lesson, cannot provide this moment of realization, as she is aware of the inequity among the social classes.