Papacy
Luke 22:31-32
Simon, Simon, behold Satan hath desired to have you, that he may sift you as wheat: But I have prayed for thee, that thy faith fail not: and thou, being once converted, confirm thy brethren.
Context of the passage
During the Last Supper discourse, Jesus warns of the coming trial of the apostles and singles out Simon Peter for a special prayer of preservation.
Catholic reading
Christ prays specifically for Peter's faith and gives him the mission to 'confirm the brethren,' foreshadowing the pope's charism of strengthening the whole Church in faith, even amid personal weakness (his coming denial).
Common objection
This prayer is personal to Peter's own historical trial, not a promise about future successors.
Response
The role of 'confirming the brethren' matches the ongoing function seen in Acts, where Peter consistently speaks first and settles doctrinal disputes (Acts 15:7-11), suggesting a continuing office within the apostolic college.