Yet since the word of God is rich and, according to the judgment of Solomon, is to be "inscribed upon the heart" not simply, but doubly and "triply," let us try even now to add some things to those which were spoken a while ago according to our strength, that we may show how, "in a type of things to come," here too one goat was offered to the Lord as a victim and the other was sent away "alive." Hear in the Gospels Pilate saying to the priests and the people of the Jews: "Which of the two do you wish that I release to you, Jesus who is called Christ, or Barabbas?" Then all the people cried out that he should release "Barabbas," but hand Jesus over to death. Behold, you have the goat which was sent away "alive into the wilderness," bearing with itself the sins of the people that cried out and said: "Crucify, crucify!" This, then, is the goat sent away "alive into the wilderness," and the other is the goat that was offered to the Lord as a victim to make propitiation for sins, and made true propitiation for the peoples who believe in him. And if you should also inquire this — who it is that led this goat "into the wilderness," so that it might be proved in him also that he was washed and made clean — Pilate himself can be taken as the "man made ready." For he was the judge of that very nation, who by his sentence sent him out "into the wilderness." But hear how he was washed and made clean. When he said to the people, "Do you wish that I release to you Jesus, who is called Christ?" and all the people had cried out, saying, "If you release this man, you are no friend of Caesar," then, it says, "Pilate called for water and washed his hands before the people, saying: I am clean from the blood of this man; see you to it." So then he will be seen, with his hands washed, to have been made clean.
Source: HOMILIES ON LEVITICUS 10