My parents threw around the idea of sending me to an academy (basically a boarding school) for highschool, but decided against it for several reasons. One: It was expensive. If you have to take out any loans at all to go, you are better off saving your money for college. Chances are you will need some sort of a loan for those four years. I had a full scholarship, but still had to take out some money for living expenses. Secondly: I would have had to live there. Paying for room and board can cost and arm and a leg, and that's on top of tuition. Thirdly: My public highschool offered a fine education. If you work hard, you will be able to do just fine in public school. Additionally, highschool is really when you have to concentrate on your studies because you will be preparing for college. Of course you don't want to slack off in 8th grade either. Paying huge amounts for schooling just doesn't make sense to me unless your public school is terrible.
I learned so much from reading and studying on my own during grade school on top of what the teachers taught me. I was lucky and didn't have too many issues with the public school system. I had a couple of dud teachers, but for me paying for school before college would have been a waste. Don't get me wrong though...if your parents can afford boarding school without breaking the wallet and taking out loans, go for it.