The Catholic conception of Christs Passion and Atonement is that Christ offered Himself up in self-sacrificial love to the Father, obedient even unto death, for the sins of all men. The Father was never angry with Christ. Nor did the Father pour out His wrath on the Son. The Passion is Christs greatest act of love, the greatest revelation of the heart of God, and the glory of Christ.1 So when Christ was on the cross, God the Father was not pouring out His wrath on His Son; in Christs act of self-sacrifice in loving obedience to the Father, Christ was most lovable in the eyes of the Father. Rather, in Christs Passion we humans poured out our enmity with God on Christ, by what we did to Him in His body and soul. And He freely chose to let us do all this to Him. Deeper still, even our present sins contributed to His suffering, because He, in solidarity with us, grieved over all the sins of the world, not just the sins of the elect. Hence, St. Francis of Assisi said, Nor did demons crucify Him; it is you who have crucified Him and crucify Him still, when you delight in your vices and sins.2 The Passion is a revelation of the love of God, not the wrath of God.
"For as by one man's disobedience many were made sinners, so by one man's obedience many will be made righteous." (Rom 5:19)
By his obedience unto death, Jesus accomplished the substitution of the suffering Servant, who "makes himself an offering for sin", when "he bore the sin of many", and who "shall make many to be accounted righteous", for "he shall bear their iniquities".
Jesus atoned for our faults and made satisfaction for our sins to the Father.
One problem with the Reformed conception is that it would either make the Father guilty of the greatest evil of all time (pouring out the punishment for all sin on an innocent man, knowing that he is innocent), or if Christ were truly guilty and deserved all that punishment, then His suffering would be of no benefit to us.
A second problem with the Reformed conception is the following dilemma. If God the Father was pouring out His wrath on the Second Person of the Trinity, then God was divided against Himself, God the Father hating His own Word.
God could hate the Son only if the Son were another being, that is, if polytheism or Arianism were true.
But if God loved the Son, then it must be another person (besides the Son) whom God was hating during Christs Passion. And hence that entails Nestorianism, i.e. that Christ was two persons, one divine and the other human. He loved the divine Son but hated the human Jesus.
Hence the Reformed conception conflicts with the orthodox doctrine of the Trinity
One question, from the Reformed point of view, is: How then were our sins paid for, if Christ was not punished by the Father? Christ made atonement for the sins of all men by offering to God a sacrifice of love that was more pleasing to the Father than the combined sins of all men of all time are displeasing to Him. Hence through the cross Christ merited grace for the salvation of all men. Those who refuse His grace do not do so because Christ did not die for them or did not win sufficient grace for them on the cross, but because of their own free choice.Please do Note -- your statement in post 962 It no longer believes in the atonement of Christ. is false.