Peter, for himself and his brethren, said that they were assured of our Lord's being the promised Messiah, the Son of the living God. This showed that they believed Jesus to be more than man. Our Lord declared Peter to be blessed, as the teaching of God made him differ from his unbelieving countrymen. Christ added that he had named him Peter, in allusion to his stability or firmness in professing the truth. The word translated "rock," is not the same word as Peter, but is of a similar meaning. Nothing can be more wrong than to suppose that Christ meant the person of Peter was the rock. Without doubt Christ himself is the Rock, the tried foundation of the church; and woe to him that attempts to lay any other! Peter's confession is this rock as to doctrine. If Jesus be not the Christ, those that own him are not of the church, but deceivers and deceived. Our Lord next declared the authority with which Peter would be invested. He spoke in the name of his brethren, and this related to them as well as to him. They had no certain knowledge of the characters of men, and were liable to mistakes and sins in their own conduct; but they were kept from error in stating the way of acceptance and salvation, the rule of obedience, the believer's character and experience, and the final doom of unbelievers and hypocrites. In such matters their decision was right, and it was confirmed in heaven. But all pretensions of any man, either to absolve or retain men's sins, are blasphemous and absurd. None can forgive sins but God only. And this binding and loosing, in the common language of the Jews, signified to forbid and to allow, or to teach what is lawful or unlawful.
Matthew Henry's Commentary on Matthew 16:20
Commentary on Matthew 16:13-20
(Read Matthew 16:13-20)
Peter, for himself and his brethren, said that they were assured of our Lord's being the promised Messiah, the Son of the living God. This showed that they believed Jesus to be more than man. Our Lord declared Peter to be blessed, as the teaching of God made him differ from his unbelieving countrymen. Christ added that he had named him Peter, in allusion to his stability or firmness in professing the truth. The word translated "rock," is not the same word as Peter, but is of a similar meaning. Nothing can be more wrong than to suppose that Christ meant the person of Peter was the rock. Without doubt Christ himself is the Rock, the tried foundation of the church; and woe to him that attempts to lay any other! Peter's confession is this rock as to doctrine. If Jesus be not the Christ, those that own him are not of the church, but deceivers and deceived. Our Lord next declared the authority with which Peter would be invested. He spoke in the name of his brethren, and this related to them as well as to him. They had no certain knowledge of the characters of men, and were liable to mistakes and sins in their own conduct; but they were kept from error in stating the way of acceptance and salvation, the rule of obedience, the believer's character and experience, and the final doom of unbelievers and hypocrites. In such matters their decision was right, and it was confirmed in heaven. But all pretensions of any man, either to absolve or retain men's sins, are blasphemous and absurd. None can forgive sins but God only. And this binding and loosing, in the common language of the Jews, signified to forbid and to allow, or to teach what is lawful or unlawful.