Professor Jay Greene throws cold water on that selectivity argument:
Surprising as it may be, most private schools are not very selective. A study of the nation's Catholic schools concluded that the typical institution accepted 88 percent of the students who applied. Other research in D.C., Dayton, and New York private schools found that only one percent of parents reported their children were denied admission because of a failed admissions test. Moreover, the academic and demographic backgrounds of students who use vouchers to attend private school across the country are very similar to those who don't.
Private schools don't significantly alter their student populations by expelling low-achieving or troublesome students, either. One study found that, Catholic high schools dismiss fewer than two students per year, on average. While it is true that every student is officially entitled to a publicly funded education, students in public schools are regularly expelled. According to the U.S. Department of Education, roughly one percent of all public school students are expelled in a year, and an additional 0.6 percent are segregated into specialized academies. That's more than in Catholic and other private schools. Moreover, public schools actually contract out 1.3 percent of their disabled students to private schools.