I think his point is that he doesn't want those that are going to send to private school regardless to get vouchers.
Obviously people that end up sending to private schools prefer to send anyway. Just like many that send to public schools prefer to send anyway (and would presumably pay for it if it costed money). Why should the government subsidize one choice but not the other? Won’t this equalize the playing field and allow all parents,
especially the ones who can least afford it, the liberty to choose what they feel is best for their children?
Of course if it were completely free it would be completely equal. So you shouldn’t consider a partial victory a victory at all?