It's doubtful that a catholic parochial school has ever turned away a catholic student. Certainly if that happens, it must be rare. If catholic students are superior to non-catholics, through some self-selection process, how does that invalidate his point? They're not being picky intentionally. A great many admit non-catholic students, often on scholarship, those students also tend to do well.
Public schools have to take children that do not want to be there and make it everyone's problem, and their classmates suffer for it. Maybe this public school policy is the issue that should concern you.
I would imagine that catholic parochial schools are selecting for parents that bother to put in the effort to swap their kids from the default, free public schools to the catholic schools.
That is entirely my point. Catholic schools aren’t doing anything special they are just not keeping the problem kids. Why do you assume this doesn’t concern me?