“Behold, I am laying in Zion a stone,
a cornerstone chosen and precious,
“The stone that the builders rejected
“A stone of stumbling,
and a rock of offense.”
9 But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light. 10 Once you were not a people, but now you are God's people; once you had not received mercy, but now you have received mercy.
1 Peter 2:4-10
The apostle Peter says there that Jesus is the cornerstone upon which the church is built (vs. 6,7). This means that Jesus is where we trace the church to, not Peter. This is an important fact because the entire Roman Catholic tradition of the papacy finds its basis in the idea that Peter was the rock upon which the church was built, and thus there is a supposed succession of a head honcho churchman.
But Peter flatly contradicts this type of thinking by making it exceedingly clear that it is Jesus upon whom the church is built. All believers are "living stones" used for the building of God's church. The apostles, being the first believers, form a proverbial base layer or foundation for this church (I believe this is what Jesus meant in Matthew 16:18). They serve an invaluable role, even now as we read the book of Acts and early church history, we may look to their example. We read the New Testament and from the apostles receive the written words that describe the living Word. We see Jesus through them, and learn how to live in light of who he is by the instructions they left in the form of letters like 1 Peter. But there is no magical line of Peter. Jesus is the cornerstone, and all the church form his holy people.
How do we know this? Peter refers to Christians in general as a "royal priesthood." This means that we don't need another human priest for confess our sins to, intercede with God for us, or administer sacraments. We are the people of God and God's Son, Jesus, serves as our merciful and sympathetic high priest (Hebrews 4:14-16).
God does establish structure for his church, including the governorship of elders over local congregations (Peter addresses them specifically in chapter 5). But this must not be mistaken as letting Christians off the hook on holiness (1:15) or of creating a special class of Christians. We all are part of the people who have now obtained mercy. A mercy dispersed by God, not by a man-made priesthood.