What does the mercy of God mean if the full punishment for sin was in fact meted out? The fullness of God's divine wrath was not withheld but redirected to a third party, an innocent party. How is that either just or merciful? This leads to another problem: the full punishment for sin is not simply death; it is eternal separation from God in hell, not three days in the tomb. If Christ was punished for all of the sins committed by all human beings of all time, then doesn't that give us a license to sin? God would be unjust to punish both us and Christ for the same sin, and since Christ has already been punished, he could not in justice punish us as well. There are only two ways to resolve this dilemma: Universalism, the "All Dogs go to Heaven" theory of salvation, or John Calvin's double pre-destination, where Christ only died to save the elect and the damned are predestined for hell, leaving the elect free to sin with impunity.
The biggest problem with the penal substitution theory for Catholics is that it leaves no room for a perpetual, propitiatory sacrifice for our sins. If Christ died on the cross to accept the punishment for sins for all men in all times and places, then why would we need to continually re-present that sacrifice to God? We wouldn't. So then why would Catholics need to go to Mass at all? These days we tend to emphasize the subjective benefits of going to Mass: we go to receive our Blessed Lord in Holy Communion, and to worship in common with the whole mystical Body of Christ, our brothers and sisters in the faith. That isn't wrong but we are omitting something important. Consider this: it is a precept of the Church that Catholics are to attend Mass every Sunday and Holy Day of Obligation (going to Mass more often is praiseworthy). It is also a precept that we are to receive Holy Communion at least once a year (again, receiving more often is praiseworthy and to be encouraged).
We must attend Mass every Sunday but we are not obligated to receive Holy Communion every Sunday. In practice, many Catholics have inverted this: the so-called "Christmas and Easter" Catholics who haven't darkened the doorway of a confessional in decades but still happily tromp up to receive communion at weddings and funerals. The reason for the precepts is that the Mass is not primarily about the subjective benefits we receive. It is to give God the honor that he is due. This is what Catholics mean when we speak of "the Sacrifice of the Mass." It is a propitiatory unbloody re-presentation of the bloody sacrifice of Calvary offered to God. Jesus Christ was both the high priest and the sacrifice as the letter to the Hebrews tells us. The priest, acting in persona Christi, becomes the offerer and the offered at every Mass every Sunday. Today I believe there is an upside-down emphasis on the communal meal aspects of the Mass at the expense of the traditional understanding of the Mass as a sacrifice. If the penal substitution theory is true, then it makes sense that we should think of the Mass as only a Communion Service for the benefit of the community.
So if penal substitution is incorrect, what is the correct Catholic understanding of the atonement? It's known among theology nerds as the satisfaction theory. At a superficial glance, the satisfaction theory appears similar to penal substitution, but there are vital differences. That deserves its own post, but in the mean time the decrees of the Council of Trent about the sacrificial nature of the Mass provide some enlightenment on divine satisfaction:
CANON I.--If any one saith, that in the mass a true and proper sacrifice is not offered to God; or, that to be offered is nothing else but that Christ is given us to eat; let him be anathema.
CANON III.--If any one saith, that the sacrifice of the mass is only a sacrifice of praise and of thanksgiving; or, that it is a bare commemoration of the sacrifice consummated on the cross, but not a propitiatory sacrifice; or, that it profits him only who receives; and that it ought not to be offered for the living and the dead for sins, pains, satisfactions, and other necessities; let him be anathema.
And of course St. Thomas:
Christ's Passion is in two ways the cause of our reconciliation to God. In the first way, inasmuch as it takes away sin by which men became God's enemies, according to Wisdom 14:9: "To God the wicked and his wickedness are hateful alike"; and Psalm 5:7: "Thou hatest all the workers of iniquity." In another way, inasmuch as it is a most acceptable sacrifice to God. Now it is the proper effect of sacrifice to appease God: just as man likewise overlooks an offense committed against him on account of some pleasing act of homage shown him. Hence it is written (1 Samuel 26:19): "If the Lord stir thee up against me, let Him accept of sacrifice." And in like fashion Christ's voluntary suffering was such a good act that, because of its being found in human nature, God was appeased for every offense of the human race with regard to those who are made one with the crucified Christ in the aforesaid manner (1, ad 4).
H/T: Unam Sanctam Catholicam