Because private school classes are small, your child cannot hide in the back of the class. If she does not understand a math concept, the teacher will probably discover that pretty quickly. He can address that learning issue on the spot, rather than waiting weeks or months to fix it.
The teacher can give each student the individual attention they deserve.
Seeing your math teacher coaching the basketball team and sharing the same passion for the sport that you have, well that makes a huge impression on a young mind. In a private school, teachers have the opportunity to be exemplars in many things.