The word of the Lord is rich, and according to the opinion of Solomon, "it must be written on the heart" not once but also twice and "three times." Let us to the best of our ability also now attempt to add something to what was said long ago. Let us show how "as a type of things to come" this one male goat was sacrificed to the Lord as an offering and the other one was sent away "living." Hear in the Gospels what Pilate said to the priests and the Jewish people: "Which of these two do you want me to send out to you: Jesus, who is called the Christ, or Barabbas?" Then all the people cried out to release Barabbas and to hand Jesus over to be killed. Look, you have a male goat who was sent "living into the wilderness." He carried with him the sins of the people who cried out and said, "Crucify, crucify!" The first is a male goat sent "living into the wilderness." The second is the male goat that was offered to God as an offering to atone for sins. Christ made a true atonement for those who believe in him.
Source: HOMILIES ON LEVITICUS 10.2.2