Objection 1. It would seem unfitting that Christ should suffer at the hands of the Gentiles. For since men were to be freed from sin by Christ's death, it would seem fitting that very few should sin in His death. But the Jews sinned in His death, on whose behalf it is said (Matthew 21:38): "This is the heir; come, let us kill him." It seems fitting, therefore, that the Gentiles should not be implicated in the sin of Christ's slaying.
Objection 2. Further, the truth should respond to the figure. Now it was not the Gentiles but the Jews who offered the figurative sacrifices of the Old Law. Therefore neither ought Christ's Passion, which was a true sacrifice, to be fulfilled at the hands of the Gentiles.
Objection 3. Further, as related John 5:18, "the Jews sought to kill" Christ because "He did not only break the sabbath, but also said God was His Father, making Himself equal to God." But these things seemed to be only against the Law of the Jews: hence they themselves said (John 19:7): "According to the Law He ought to die because He made Himself the Son of God." It seems fitting, therefore, that Christ should suffer, at the hands not of the Gentiles, but of the Jews, and that what they said was untrue: "It is not lawful for us to put any man to death," since many sins are punishable with death according to the Law, as is evident from Leviticus 20.
On the contrary, our Lord Himself says (Matthew 20:19): "They shall deliver Him to the Gentiles to be mocked, and scourged, and crucified."
I answer that, The effect of Christ's Passion was foreshown by the very manner of His death. For Christ's Passion wrought its effect of salvation first of all among the Jews, very many of whom were baptized in His death, as is evident from Acts 2:41 and Acts 4:4. Afterwards, by the preaching of Jews, Christ's Passion passed on to the Gentiles. Consequently it was fitting that Christ should begin His sufferings at the hands of the Jews, and, after they had delivered Him up, finish His Passion at the hands of the Gentiles.
Reply to Objection 1. In order to demonstrate the fulness of His love, on account of which He suffered, Christ upon the cross prayed for His persecutors. Therefore, that the fruits of His petition might accrue to Jews and Gentiles, Christ willed to suffer from both.
Reply to Objection 2. Christ's Passion was the offering of a sacrifice, inasmuch as He endured death of His own free-will out of charity: but in so far as He suffered from His persecutors it was not a sacrifice, but a most grievous sin.
Reply to Objection 3. As Augustine says (Tract. cxiv in Joan.): "The Jews said that 'it is not lawful for us to put any man to death,' because they understood that it was not lawful for them to put any man to death" owing to the sacredness of the feast-day, which they had already begun to celebrate. or, as Chrysostom observes (Hom. lxxxiii in Joan.), because they wanted Him to be slain, not as a transgressor of the Law, but as a public enemy, since He had made Himself out to be a king, of which it was not their place to judge. Or, again, because it was not lawful for them to crucify Him (as they wanted to), but to stone Him, as they did to Stephen. Better still is it to say that the power of putting to death was taken from them by the Romans, whose subjects they were.
Source: Summa Theologica (New Advent)