The answer to this question takes us back to John 13:37-38,

Peter asked, “Lord, why can’t I follow you now? I will lay down my life for you.” Then Jesus answered, “Will you really lay down your life for me? Very truly I tell you, before the rooster crows, you will disown me three times!

Jesus' three questions, "Do you love Me?", may correspond to Peter's three denials of Jesus: "I don't know you." Jesus' first question, "Do you love me more than these?" may correspond to Peter's proud assertion, "I will lay down my life for you" (John 13:37). Matthew adds to the account that Peter also said, "Even if all fall away on account of you, I never will" (Matthew 26:33). So Peter was asserting that he would be more devoted than the other disciples. But his denials would make him out to be quite the opposite of his assertion.

What is also telling about Jesus' questions are the commands that follow Peter's reaffirmation of his devotion. Jesus says, "Feed my sheep... Take care of my sheep... Feed my sheep" (John 21:15-17). It is almost as though Jesus is telling Peter, "Don't just say you love me, show it by your obedient actions." This is consistent with Jesus' repeated emphasis on obedience over lip service (cf. Matthew 21:28-31; 15:7-8; 23:1-3).

Now, some have tried to argue that while Jesus was calling Peter to a higher-level love (agapao), Peter was responding sheepishly that he could commit to a lower-level love (phileo) for Jesus. This conclusion arises out of the different Greek words used for love by Jesus and Peter. While even a cursory search on the internet will show how widespread this view is, true Greek scholars seem very divided over the matter, and the larger context of use suggests that these terms were used interchangeably in parallel texts. Consider these examples:

Uses agapao	Uses phileo
John 3:35 - "The Father loves the Son..."	John 5:20 - "For the Father loves the Son..."
John 13:32 - "The disciples whom Jesus loved..."	John 21:20 - "...the disciple whom Jesus loved..."
Luke 11:43 - "...you love the most important seats"	Matthew 23:6 - "...the love the place of honor..."
Gen 37:3 - "Israel loved Joseph more than any of his other sons"	Gen 37:4 "their father loved him more than any of them"

 

Perhaps the most compelling argument may be that Peter does not recognize the distinctions in the terms used for love by Jesus and himself. The narrator simply informs us that Peter felt bad because Jesus asked him three times. 

What this means is that we ought not to make too much of the interchange of Greek terms or even the meaning of one Greek term for love over another. The use of the different terms may, therefore, simply be for stylistic variation rather than to bring out subtleties in meaning. This also suggests, as my Greek professors often told me, those that have just some knowledge of Greek may do more harm to correct biblical interpretation than those that have no knowledge at all.

Unfortunately, many that often press these distinctions have a very rudimentary knowledge of the Greek Bible and, therefore, make inaccurate assertions in their ignorance, laziness or pride. Let me emphasize again, more important than knowing Greek is knowing the context. Therefore, let us humbly, diligently, and correctly handle God's Word:

Do your best to present yourself to God as one approved, a worker who does not need to be ashamed and who correctly handles the word of truth (2 Timothy 2:15).