Bad or mediocre private schools—which are the vast majority—pay less than public schools. Good ones may pay more. Teaching in private schools also tends to be

Bad or mediocre private schools—which are the vast majority—pay less than public schools. Good ones may pay more. Teaching in private schools also tends to be an easier job, mainly thanks to selection bias giving you an easier set of students to teach, and (oddly enough) school admin being both willing and able to tell parents to fuck off and go away if they or their children are being jackasses and won't shape up. Public schools can't do that. Turns out decent-or-better private schools would rather lose one paying student than let them make things worse for the rest, risking several paying students (and the good ones all have waiting lists anyway—they'll fill the slot, no problem).