What follows is from Chapter 4 of his work, “Matthew in History: Interpretation, Influence, and Effects” (Minneapolis, MN: Augsburg Fortress Press ©1994), Chapter Four: “Peter: The True Christian or the Pope (Matthew 16)”:
There are four main types of interpretations of Matt. 16:18 in the history of exegesis.
1. The first is the typological interpretation, which is not only the oldest that we know but the “mother” of two other types of interpretation. We could call it the “democratic” interpretation of Matt. 16:18. Its classical representative is Origen. According to him, Peter symbolizes every true, spiritual Christian. He says, “A rock is every disciple … who drank of the spiritual Rock [Christ], who followed them” (1 Cor 10:4 [citing Origen’s Commentary on Matthew 12.10]). Elsewhere Origen says that the church is built on the word in every human being, and, in this way, every Christian becomes strong like a rock [citing Contra Celsum 6.77]. According to this interpretation, Peter is the type of the true, spiritual, and perfect Christian.