In actual fact, the majority of church fathers interpret the "rock" as the faith Peter had in Christ.
As you are not Protestant I'm surprised you fell into their either/or thinking. I thought you would see Catholic both/and thinking.....especially here.
The Fathers
also saw Peter as the rock.
As indeed Protestant scholars do today.... Here is a selection.......
Trevor G. Jalland, PhD (Anglican)
“The solemn words…proclaim in effect that the eponym now bestowed upon Simon is no mere nickname like Boanerges (son of thunder), ‘Petra’ (Kepha) literally denotes the apostle himself as ‘Rock”, and it is on Peter as on rock that the foundations of the new ekklesia, described in the metaphor of a building, are to be laid. Against that building so erected, in virtue of the immovable nature of the substance on which its foundations rest, neither the forces of evil nor of death can ultimately prevail.” (Jalland, Trevor G., The Church and the Papacy, London: SPCK, 1946, page 55)
Donald A. Carson (Baptist)
“On the basis of the distinction between 'petros' . . . and 'petra' . . . , many have attempted to avoid identifying Peter as the rock on which Jesus builds his church. Peter is a mere 'stone,' it is alleged; but Jesus himself is the 'rock' . . . Others adopt some other distinction . . . Yet if it were not for Protestant reactions against extremes of Roman Catholic interpretation, it is doubtful whether many would have taken 'rock' to be anything or anyone other than Peter . . . The Greek makes the distinction between 'petros' and 'petra' simply because it is trying to preserve the pun, and in Greek the feminine 'petra' could not very well serve as a masculine name . . . Had Matthew wanted to say no more than that Peter was a stone in contrast with Jesus the Rock, the more common word would have been 'lithos' ('stone' of almost any size). Then there would have been no pun - and that is just the point! . . . In this passage Jesus is the builder of the church and it would be a strange mixture of metaphors that also sees him within the same clauses as its foundation . . .” (Expositor's Bible Commentary, [Grand Rapids, MI: Zondervan, 1984], vol. 8: Matthew, Mark, Luke (Matthew: D.A. Carson), 368)
"The word Peter petros, meaning 'rock,' (Gk 4377) is masculine, and in Jesus' follow-up statement he uses the feminine word petra (Gk 4376). On the basis of this change, many have attempted to avoid identifying Peter as the rock on which Jesus builds his church yet if it were not for Protestant reactions against extremes of Roman Catholic interpretations, it is doubtful whether many would have taken 'rock' to be anything or anyone other than Peter." (Carson, Zondervan NIV Bible Commentary [Zondervan, 1994], volume 2, page 78, as cited in Butler/Dahlgren/Hess, page 18)
Oscar Cullman (Lutheran)
"The obvious pun which has made its way into the Gk. text as well suggests a material identity between petra and petros, the more so as it is impossible to differentiate strictly between the meanings of the two words. On the other hand, only the fairly assured Aramaic original of the saying enables us to assert with confidence the formal and material identity between petra and petros: petra = Kepha = petros....Since Peter, the rock of the Church, is thus given by Christ Himself, the master of the house (Is. 22:22; Rev. 3:7), the keys of the kingdom of heaven, he is the human mediator of the resurrection, and he has the task of admitting the people of God into the kingdom of the resurrection...The idea of the Reformers that He is referring to the faith of Peter is quite inconceivable in view of the probably different setting of the story...For there is no reference here to the faith of Peter. Rather, the parallelism of 'thou art Rock' and 'on this rock I will build' shows that the second rock can only be the same as the first. It is thus evident that Jesus is referring to Peter, to whom He has given the name Rock. He appoints Peter, the impulsive, enthusiastic, but not persevering man in the circle, to be the foundation of His ecclesia. To this extent Roman Catholic exegesis is right and all Protestant attempts to evade this interpretation are to be rejected." (Cullmann, article on "Rock" (petros, petra) trans. and ed. by Geoffrey W. Bromiley, Theological Dictionary of the New Testament [Eerdmans Publishing, 1968], volume 6, page 98, 107, 108)
Ivor H. Jones (Methodist)
"...in 16.18 Peter is the rock on which the new community could be built, as Abraham was described in rabbinic writings as the rock on which God could erect a new world to replace the old....The arguments have raged across the centuries over the phrase 'on this rock' : does it mean on Peter, or on Peter's confession? But the text is clear: Peter was divinely inspired and this was the reason for his new function and the basis of his authorization. His function was to provide for Jesus Christ the beginnings of a stronghold, a people of God, to stand against all the powers of evil and death...They are God's people, the church...as the church they represent God's sovereign power over evil (18.18b) and rely upon a new kind of divine authorization...This authorization is given to Peter; so Peter is not only a stronghold against evil; he also is responsible for giving the community shape and direction." (Jones, The Gospel of Matthew [London: Epworth Press, 1994], page 99)
David Hill (Presbyterian)
“On this rock I will build my church: the word-play goes back to Aramaic tradition. It is on Peter himself, the confessor of his Messiahship, that Jesus will build the Church. The disciple becomes, as it were, the foundation stone of the community. Attempts to interpret the “rock” as something other than Peter in person (e.g., his faith, the truth revealed to him) are due to Protestant bias, and introduce to the statement a degree of subtlety which is highly unlikely.” (The Gospel of Matthew, New Century Bible Commentary [Grand Rapids, MI: Eerdmans, 1972], 261)