John 21:17 - Albert Barnes' Notes on the Bible

The third time - It is probable that Jesus proposed this question three times because Peter had thrice denied him. Thus he tenderly admonished him of his fault and reminded him of his sin, while he solemnly charged him to be faithful and vigilant in the discharge of the duties of the pastoral office. The reason why the Saviour addressed Peter in this manner was doubtless because he had just denied him - had given a most melancholy instance of the instability and weakness of his faith, and of his liability to fall. As he had thus been prominent in forsaking him, he took this occasion to give to him a special charge, and to secure his future obedience. Hence, he so administered the charge as to remind him of his fault; and he made him so prominent as to show the solicitude of the Saviour that, henceforward, he might not be left to dishonor his high calling. This same charge, in substance, he had on other occasions given to the apostles Matthew 18:18, and there is not the slightest evidence here that Christ intended, as the Papists pretend, to give Peter any special primacy or eminence in the church. The charge to Peter arose, manifestly, from his prominent and melancholy act in denying him, and was the kind and tender means used by a faithful Saviour to keep him from similar acts in the future dangers and trials of life. It is worthy of remark that the admonition was effectual. Henceforward, Peter was one of the most firm and unwavering of all the apostles, and thus fully justified the appellation of a rock, which the Saviour by anticipation had given him. See the notes at John 1:42.