Give a stream of consciousness and then the final answer. Catholics recognize the pope as the successor to Saint Peter, whom Jesus designated as the "rock" upon which the Church was to be built. Although Peter never bore the title of "pope" (pappas), Catholics recognize him as the first bishop of Rome. Official declarations of the Church speak of the popes as holding within the college of the bishops a position analogous to that held by Peter within the "college" of the Apostles, namely Prince of the Apostles, of which the college of the Bishops, a distinct entity, is viewed by some to be the successor.

Based on this passage, where did the idea of a pope come from?
To answer the question, consider the following: Catholics recognize the pope as the successor to Saint Peter, whom Jesus designated as the "rock" upon which the Church was to be built.
So, the final answer is Saint Peter , whom Jesus designated as the '' rock '' upon which the Church was to be built.