The Apostle Peter was not the first pope. He did not consider himself to be the single chief authority of the church on Earth. Rather, he considered himself to be one of many church leaders:
“To the elders among you, I appeal as a fellow elder and a witness of Christ’s sufferings who also will share in the glory to be revealed.” (I Peter 5:1).
Notice that he refers to himself as an “elder” or “Presbyter.” By doing this he is rejecting the idea of a one man Bishop that rules over a particular diocese. In the Bible the word Bishop (Episcopos) and Elder (Presbyter) are used interchangeably. Later on the bishops gained authority over the presbyters. But Peter calls himself a Presbyter instead of an Episcopos. He is willing to use the same title as the rest of the church leaders, and thus rejecting a special position at the top of the hierarchy.