It is a catch 22 situation. Primary school lays the foundation for solid achievement in high school, while high school lays the foundation for solid achievement in college. If either foundation is constructed with less than the best materials, the structure built on that foundation will have deficiencies.
Primary grades build the foundation. Since most parents can more easily monitor and help with learning in the primary grades, sending your child to a good public school for the early years makes sense. The important thing any parent must do for her young child is to engage it in a wide variety of stimulating activities, such as reading, solving puzzles, making music, art and so on. Limiting television and video game time and teaching your child to entertain itself with non-electronic activities is a good thing. The problem is that many parents feel they have to sacrifice quality time with their children for their careers and jobs. That is a very tough call. If you can afford to stay home with your child while it is young, you can shape that young mind yourself instead of leaving that critical task to others. After all, you are particular about what food your child eats. Shouldn't you be just as particular about what ideas and facts your child's mind is fed?
High school subjects require specialist knowledge. On the other hand, high school subjects, especially those being taught at the AP level, are intensive and quite complicated. Most of us will find Mandarin, Latin or calculus a bit beyond our expertise. The highly trained teachers a good prep school affords know how to teach those subjects and prepare your child properly for the national examinations colleges and universities will expect.
If you have to make a choice, invest in prep school. If you don't have to make a choice, invest in private education from kindergarten on up. You will not regret it.