They weed out hard-to-teach students, the author says, which means it will drive down the cost of teaching in private schools (less "hand holding" of bad students means fewer teachers required) while raising the cost in municipal schools at the same time, because the municipal schools basically get all the "bad students" which require additional hand holding.
Furthermore, if you outright reject "bad students" - where "bad" may mean intellectually bad, socially bad, bad economic background, disabled ("with diagnosis"), etc - then you can later claim in your marketing materials that students in your private school are performing above average.
It probably will also lower administrative burden, as the "easy" students are less likely to get in major trouble, are less likely to need involvement of the school and child protected services in their lives, the teachers go to court as a witness in child abuse cases less, etc.
And of course, you can always simply pay teachers less than in municipal schools - which is one of the claims of the author as well.
And the last claim the author made is that a lot of these companies just hire some under-qualifiied teachers whenever they can get away with it.
I have to admit, the author makes a lot of sense to me.