No worries bursting my bubble, I learned a bunch, so that was cool. I'll have to take a look at the private K-12 schools in my area. I assumed they were going to the benefit of whoever owned the schools.
As a former K-12 private schooler, the one I went to was non-profit. It eventually went out of business due to being run a little bit too non-profit even though it existed for 20 years. I really enjoyed my time there and was sad to see it go out of business.
Many private schools are not profitable institutions by a long shot. They could use a little bit more profit motive sometimes.
Many private schools are either:
* some religious institution, like a catholic school
* some really old private school that has kept on going because it's where all the rich kids go to with a relatively large endowment.
* opening with a specific charter in mind, like a sudbury school