Papal primacy is the pope’s authority and universal jurisdiction over the Church. There were many controversies due to Christ’s commissioning of Peter to be the visible head of the Church. Which resulted in the first Vatical council defining the papal infallibility.
(Mt.16:18)You are Peter and on this rock I will build my Church."Since Peter was made the foundation of the Church,it gave him a primacy among the apostles. All popes that come along become successors of St. Peter.
The teachings of the second Vatican council emphasized that all the bishops and authority is from the pope. Vatican II reaffirmed, the teaching of Vatican I on papal authority. While Vatican I dealt with notably, infallibly declaring papal infallibility.