Dedicated staff, donations, including 30 hours/year of parent time/household doing things which free up teachers to teach. Parental involvement is a big factor.
Kids actually interested in learning. Less bullsh*t in dealing with the administration. The right to banish disruptive kids.
...add in parents with obvious 'skin in the game'.
They care enough that their children get a decent education they are willing to shell out extra for that, and as such they place value on that education.
In that sort of home environment, it is more likely the child will be supervised at home, will learn, will not be a discipline problem, etc.--many of the critical elements missing from public schools, along with the parochial/private emphasis on achievement versus the public school 'crab basket' inertia against it.
It is not strictly a 'teacher' problem--the schools have different worldviews, especially since prayer was forced out of the public schools (prayer which was always optional for those who chose not to--they just did not say them).
You have to ask yourself how do private schools turn out smarter students than public schools and pay their teachers less. It’s a great argument to use.