Jamieson, Fausset and Brown on Matthew 16:19

19. And I will give unto thee the keys of the kingdom of heaven--the kingdom of God about to be set up on earth

and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven--Whatever this mean, it was soon expressly extended to all the apostles (Mt 18:18); so that the claim of supreme authority in the Church, made for Peter by the Church of Rome, and then arrogated to themselves by the popes as the legitimate successors of St. Peter, is baseless and impudent. As first in confessing Christ, Peter got this commission before the rest; and with these "keys," on the day of Pentecost, he first "opened the door of faith" to the Jews, and then, in the person of Cornelius, he was honored to do the same to the Gentiles. Hence, in the lists of the apostles, Peter is always first named. See on Mt 18:18. One thing is clear, that not in all the New Testament is there the vestige of any authority either claimed or exercised by Peter, or conceded to him, above the rest of the apostles--a thing conclusive against the Romish claims in behalf of that apostle.