I don't think there is anything wrong. Private schools are a business. While most are ostensibly non-profit, those providing initial funding want the school to be a sustainable business, which means that they must at a minimum cover their costs. And you certainly want the school to be able to attract highly talented teachers, and that drives up tuition costs as well. Given all that, if the school is good, I think that $16K per year is actually very reasonable.

Your other alternative is to live in a city with outstanding public schools. They certainly exist, but you will generally find that the home prices are higher as a result because of the school quality. However, your higher mortgage costs will probably still work out cheaper than private school tuition.