Continuing to reveal the fruits of my research, here is what David L. Turner from the Baker Exegetical Commentary wrote:
Although some Protestants disagree (see esp. Caragounis 1989), Jesus plays on the nickname Peter in speaking of him (as spokesman for the disciples) as the foundation of the nascent church (cf. Eph. 2:20; Rev. 21:14). This more natural understanding of Jesus’ words is preferable to other views that take the rock to be Jesus or Peter’s confession of Jesus. The “gates of hades” probably allude to biblical “sheol” as the domain of Satan and death. Jesus promises that the evil powers arrayed against it will not destroy the church that he will build on the foundation of Peter and the apostles.
Since the Reformation, 16:18 has loomed large in discussions between Protestants and Roman Catholics. In response to the Roman Catholic teaching about Peter as the first pope and about apostolic succession, many Protestants have argued that Jesus did not mean that Peter was the rock. It has been suggested that Jesus was speaking of himself (Lenski 1961: 626; Walvoord 1974: 123; Wilcox 1975) or of Peter’s confession (most credibly argued by Caragounis 1989; cf. Calvin 1972: 2.188; McNeile 1915: 241; Toussaint 1980: 201-2) as the foundation of the church. Gundry (1994: 334-35) argues that 16:18 alludes to 7:24 and that Jesus means that he will build his church on his own words. But the distance of 7:24 from 16:18 renders such an allusion extremely subtle at best. It is also argued that Peter cannot be the rock, since the name Peter (Petros) is masculine and the word rock (petra) is feminine. But grammatical precision is not required in metaphors such as this. Another argument is that Peter is not the foundation of the church because petra means bedrock and petros means an individual stone. But this extremely subtle distinction would make metaphorical speech impossible. Jesus is speaking of Peter in 167:18 just as clearly as Peter is speaking of Jesus in 16:16 (France 1985: 254).
In the NT, the “foundation” metaphor refers to Jesus’ teaching (7:24), Jesus himself (1 Cor. 3:10), Jesus’ apostles (Eph. 2:20; Rev. 21:14), and repentance (Heb. 6:1). The context of a metaphor determines the entity to which it points. Here Jesus’ response to Peter’s confession is a pun, or paronomasia, on the nickname he has evidently just given Peter (Matt. 4:18; 10:2). The pun concerns Peter’s unique role as the model disciple in Matthew. Peter’s future role as preacher to Jews and Gentiles (Acts 2,10) is also projected here. Jesus is not speaking of himself as the foundation of the church, since he describes himself as the builder. Neither is Peter’s apostolic confession the foundation of the church –he, as the confessing apostle, is that foundation. And it is not Peter alone but as first among equals, since the context makes it clear that Peter is speaking for the apostles as a whole in Matt. 16:16 (D. Turner 1991; Viviano 1990b: 660). This best fits the Matthean context, and it also coheres with other NT texts that speak of an apostolic foundation for the church (Eph. 2:20; Rev. 21:14). The Baptist scholar J. Broadus (1886: 355-58) recognized this 120 years ago, and most of the recent evangelical commentators on Matthew concur.
The real difficulty Protestants have with the Roman Catholic teaching concerning Peter is the notion of sole apostolic succession emanating from Peter as the first bishop of Rome (Calvin 1972: 2.189-90); Morris 1992; 424). This dogma is anachronistic for Matthew, who knows nothing about Peter being the first pope or of the primacy of Rome over other Christian churches. Matthew would not have endorsed the idea of Peter’s infallibility or sole authority in the church, since Peter speaks as a representative of the other apostles and often makes mistakes.
More to come…