Private schools can fire teachers subjectively. A good private school principal can use gut feel to evaluate a teacher. But that doesn't scale, unless we find a way to identify and recruit very smart, very trustworthy principals on a large scale.
People are emotionally averse to firing others they may have been working with for years, and there's not a good enough reason to fire someone in a private organization unless they affect the bottom line, and outside of exceptional cases I don't see how the bottom line changes much based on individual teachers. You're probably not going to quit private school based on any one single teacher.
You need a strong economic incentive for the organization in order for the "fire more easily" idea to work. For instance, if a private school got paid according to the competitiveness of the college the student is accepted into.
I remember reading an article (linked from HN I believe) that was a response to the "Waiting for Superman" movie which cited numbers showing that private schools didn't perform any better than public schools. That would suggest that either the ability to fire teachers subjectively doesn't have an impact on student performance, or that private schools don't fire enough teachers or the metrics the private schools use to fire teachers are not in line with what would improve student achievement.
