I'd agree that on average private schools are no better than public schools. The advantage of sending your kid to a private school is that you get to select the school though, so you can pick a better one.
I think one problem with the education system in the US, particularly as it relates to student debt, is that a lot of people go to college just because it's what you do after high school and ultimately end up working in jobs that don't actually need a degree. Education for its own sake is certainly a worthy cause, and going to college can be a great life experience, but it creates economic problems that I don't know are justified. I think a lot of this though is a product of our parents' and grandparents' generations, when sending your kids to college first became an attainable goal for the average family and everyone knew that sending your kids to college is how they could get the Good Jobs like doctor, lawyer, etc. The problem is, you can't have a society composed entirely of doctors and lawyers, and people go get these expensive degrees and there aren't enough jobs in those fields to go around. (Just using doctor and lawyer as examples, but really it encompasses a lot more than that.)
Related to that problem is that it seems that most high schools focus almost exclusively on college prep, and don't provide a practical education. The problem with that is three-fold: one, I believe it encourages drop-outs because kids who know they aren't going to college don't see any benefit in finishing high school; two, the kids who DO finish but don't go to college haven't been taught anything useful; and three, it reinforces the idea that college is just what you do after high school, encouraging people to go who don't need to. High schools should definitely provide college prep, because some people are going to go to college and they need to be prepared, but that shouldn't be all they provide; they should also provide courses to prepare kids for careers that don't involve a college degree. I mentioned welding before: that's a highly skilled task that requires training, but you don't need a college degree to be a welder, and you should be able to learn to weld in high school. Even a middle ground, with better preparation for kids going to technical schools to learn to be auto mechanics or whatever. I don't even think my high school had an auto shop...
Anyway, that's my rambling. I'm just going to trail off here cause I've kind of run out of things to say.