That's Calvinism or Jansenism, not Catholicism. If you follow it to its logical conclusion, you must embrace double predestination -- that those who are damned are damned because God positively wills and chooses it. (Unless of course you want to be a Universalist.)
St. Paul says this is flatly wrong when he teaches that the "wages of sin is death, but the gift of God is life on high in Christ Jesus". Damnation is earned; salvation is free. Double predestination makes both damnation and salvation "free," the only question is to which group God has assigned you.
Catholic dogma teaches that (a) all men are given grace sufficient to save their souls; (b) those who are reprobate earn their reprobation by resisting that grace; and (c) their resistance is of such severity that God sovereignly chooses to respect their decision to pursue evil rather than to overcome it. (Of course God has foreseen all of this from the foundation of the universe.)
Therefore the atonement is efficacious for all men, but effective only for the elect.
If Bishop Zollitsch is being quoted accurately, his teaching is not even compatible with the Nicene Creed he proclaims at Mass, which describes Jesus as "the only-begotten Son of the Father," "who for us men, and for our salvation, came down from heaven ... was made man ... suffered under Pontius Pilate ... and was buried".
Thank you for a wonderful explanation.
If. Quite possibly, he wasn't. See my previous post.