The disciples went fishing. That was after they have seen the risen Lord already twice. Peter was going fishing and the other ones were with him. They endeavored to catch fish over the night only to catch none. As the risen Lord told them to cast the net to a point, they did and they got a lot of fish—153 fish as the text says later.
John recognized that it was the risen Lord and they gathered to him. He was preparing a meal for them with fish and bread. As he had prepared the meal he invited the disciples to breakfast. And finally all the disciples recognized that it was the risen Lord. They finished the breakfast.
And Jesus asked a question to Peter, who initiated coming to fish, and who just finished breakfast to nourish the weary body after vain casting nets over the night: “Do you love me more than these?”
What are “these”? The question was asked by the Lord after Peter was reminded of the similar miraculous catching, which led him to follow Jesus as it is recorded in Luke 5:1-11. Then, Jesus told him to follow him and he would make Peter catch men. It was also after the meal of fish and bread. Fish and bread were a meal over which Jesus had a great teaching on what the work of God is that followers of him have to do as it is recorded in John 6:15-29. Peter, other disciples as well, was reminded sufficiently by the things of the teachings of the Lord. Now the Lord is asking to Peter the question, who was initiated the fishing even after the risen Lord appeared to the disciples twice.
What is ‘these’ that Jesus was referring to in the question to Peter if he loved more than him? ‘These’ refers to what Jesus reminded Peter and the disciples of—catching fish, what Peter was doing when he was called to follow Jesus, fish and bread, which Jesus rebuked his followers for they were following him to eat them, and meal, on which Jesus taught the followers that it is not what they have to work for.
Why did the Lord ask the question? Peter, who must have remembered what Jesus taught regarding ‘these’ and taught them to others, has returned to ‘these’. Now, after Jesus reminded Peter and other disciples of what he had taught, he is asking the question. Therefore, it is not actually a question but a rebuke, which is like saying, “What are you doing here; have you returned to ‘these’ because you love ‘these’ more than me?” The disciples were supposed to teach men to observe what Jesus commanded to make disciples, which is catching men metaphorically speaking (Matt. 28:19-20). But they were catching fish, for themselves. What a disappointment of the risen Lord it might be, who suffered the passion for salvation of all nations! Now, therefore, with reminding the disciples of the teachings and rebuking Peter, the Lord is restoring the disciples to their great mission—“Feed my lambs”; “Shepherd my sheep”; and “Feed my sheep”.
There seems no point to think that Jesus was making Peter compete in loving the Lord with other disciples. It makes no sense and does not have any support from any part of the Bible—God does not command any one to compete with others in loving him because everyone is supposed to love him with all heart and strength. Therefore, there is no point to understand “these” as referring to the other disciples than Peter.