At least in Maryland, one doesn't need to be certified to teach in private schools.
At my sons’ high school, only about one-fifth of the faculty have any sort of education degree, and for many of them, it is a second degree added onto a real degree, such as in math, English or history.
sitetest
The number of private schools is, unfortunately small, and unfortunately these are not free of the same “progressive” views. The top private schools need to get their students into the most prestigious schools.” and so they aim to make them attractive to such schools. If they don’t, their clients will stop paying. The best schools are not necessarily the best schools EXCEPT they bring students in contact with the right people. At Harvard, some of the brightest kinds in the country are brought together, but they get taught by TAs. J.K. Gailbraith, for one, made no secret of the fact that he didn’t like to teach undergraduates or even graduates. For the same reason, I suppose, that Babe Ruth would not have liked coaching a college baseball team, why great players seldom make good coaches. Other schools have good scholars who do like teaching. Those are hard to find. You won’t find them listed in US News.