That apostolic primacy which the Roman Pontiff possesses as successor of Peter, the prince of the apostles, includes also the supreme power of teaching. This Holy See has always maintained this, the constant custom of the Church demonstrates it, and the ecumenical councils, particularly those in which East and West met in the union of faith and charity, have declared it. -Vatican 1, Session 4, 1:1-4, 3:1 4:1 (https://www.ewtn.com/library/COUNCILS/V1.HTM)
The Roman doctrine of the papacy stands or falls on Matthew 16:13-20. We will examine this Roman Catholic dogma in three phases: first, looking at Matthew 16:13-20, second, looking at relevant New Testament passage, and third, looking at history before giving concluding thoughts.