Book 4 of 4 - External Means by which God Invites Us into the Society of Christ and Holds Us Therein
Chapter 6 - Primacy of the Roman See
1-7 - Refuting assumptions about Peter's primacy
1. Primacy of the Roman bishop as pope is central to Rome's view of the church. They define schism as leaving this authority.
2. Rome says Israel's high priest is precedent for a pope. But the high priesthood was a type of Christ (Heb 7:12), not of the pope; Christ alone has this title of high priest, since the role is one of appeasing God.
3. Christ told only Peter to feed His sheep (John 21:15), and that on Peter Christ would build His church (Matt 16:18). But Peter tells all other elders to feed Christ's sheep - 1 Pet 5:2. The power to bind and loose isn't to rule the whole world, but to preach and discipline according to the Gospel - John 20:23; 2 Cor 5:18; 10:6.
4. "Nothing is here given to Peter which was not also common to his colleagues [the apostles]." See Matt 18:18; John 20:23. Jesus didn't speak only to Peter at times in order to prefer him to the others, but to emphasize the unity of them all together.
5. Maybe the honor of first rank was given Peter, but not an authority surpassing the others.
6. Christ is the one foundation of the Church - 1 Cor 3:11.
7. Peter follows the Jerusalem council, and doesn't write alone, or by his own authority, but by the assembly's - Acts 15. His actions in Acts 8:14 show he is "not in authority over against [the other apostles]." Paul's whole point in Galatians 1-2 is that he is Peter's equal, and not subject to him - Gal 1:18; 2:8, 11-14.