John Chrysostom

For what wonder is it that this should befal Peter, who had never received a revelation concerning these things? For that you may learn that that confession which he made concerning Christ was not spoken of himself, observe how in these things which had not been revealed to him, he is at a loss. Estimating the things of Christ by human and earthly principles, he judged it mean and unworthy of Him that He should suffer. Therefore the Lord added, For thou savourest not the things that be of God, but the things that be of men.

Catena Aurea by Aquinas ↗

Theophylact of Ohrid

Then Peter took Him and began to rebuke Him, saying, Be it far from Thee, Lord, this shall not be unto Thee. Peter rightly confessed what had been revealed; in what had not been revealed, he erred: that we may learn that Peter did not utter that great truth without God's help. Not wanting Christ to suffer, and being ignorant of the mystery of the Resurrection, Peter said, "Be it far from Thee, Lord, this shall not be unto Thee."

Commentary on Matthew ↗

Jerome

And Peter took him aside and began to rebuke him, saying: Lord, be it far from you, this shall not happen to you. But he turned and said to Peter: Get behind me, Satan, you are a hindrance to me, for you are not setting your mind on the things of God, but on the things of man. We have often said that Peter had great zeal and love for the Lord Savior. …

Commentary on Matthew ↗

Hilary of Poitiers

The Lord, knowing the suggestion of the craft of the devil, says to Peter, Get thee behind me; that is, that he should follow the example of His passion; but to him by whom this expression was suggested, He turns and says, Satan, thou art an offence unto me. For we cannot suppose that the name of Satan, and the sin of being an offence, would be imputed to Peter after those so great declarations of blessedness and power that had been granted him.

Catena Aurea by Aquinas ↗