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.
First, parents are involved. When you cut a check each month for little Johnny's or Susie's education, you want your money's worth--so you're willing to make sure they do their homework, understand their lessons, and work hard to achieve even if you don't have the time/means to homeschool.
Second, that willingness to be involved, to sacrifice for the kids, indicates that the students in the private/parochial environment will be pre-screened with a bias toward children who actually have an emphasis placed on education in the home and are not just being dumped at a state-run babysitter. Children are there for a purpose, not just because the law requires them to show up.
Third, discipline can be maintained, and (especially the) Parochial schools are not as distracted with sexual/social (Marxist) themes. Dress codes/uniforms limit the amount of distraction as well.
Fourth: there is, especially in parochial schools, a different standard of decorum and respect, one which begins with either the secular authority of a non-church school and a distinct parental bias toward their child NOT getting in trouble, or which acknowledges the authority of God in the parochial schools and encourages the students to follow His will. Either way, the entire environment can be far more conducive to learning than the public schools because discipline is often based on standards which each child is encouraged to live by (self-imposed), not just live under (externally imposed).