One major reason Paul wrote "the love chapter" into 1st Corinthians was to recondition those native Greek speakers as to what "agape" could indicate, in the new Christian usage. If the word already meant such things, that chapter would not have been so radical. And as for the popular rendering, "unconditional love", excuse me, but what heathen Greek, before Jesus, ever conceived such a thing? When Jesus said, "Agapate your enemies", that was radical even for Jews! Not even Septuagint uses of Agape had conditioned this word for the meanings that Jesus and Paul brought to God's people.
"Love" may have always been the most excellent way, but- it had not yet been stated in so many words.
Meanwhile, in the minds of the people whose tongues gave us Greek, Friendship was the highest form of devotion. Period. Plato and Aristotle did no better than suggesting that "helping someone else is a way of serving oneself". The best one could aspire to was great personal loyalty, idealized by the legend of Damon & Pythias. Even non-idealized, loyal friendship was the greatest "love" any Greek speaking soul ever knew, before Christ. (That's not to knock loyalty, which remains pretty fantastic in it's own right.)
Back to proper linguistics, search the Liddell-Scott Lexicon some time for phil- stems and agap- stems, and see which word was more highly though of, not to mention more commonly used, in the classical age. Agape meant something else, like caress[ing], affection, contentment, or perhaps general positive regard. However, to be remarkably fond of something, or someone, you would be called a phil-something. In English also, Philosopher and Philharmonic are but two cognates the OED lists in its ten full pages of phil- words, to say nothing of suffixed loans such as audiophile. In both Greek and English, the phil- stem stands tallest.
Which brings us back to the reason you're still reading.
In the Gospel of John, agap- forms outnumber phil- forms (33 to 16), although the noun forms balance out (6 to 6), and there are admittedly times when the meanings may seem interchangeable. But while chapter 17 leaves no doubt that God's most Enduring Love, in the author's opinion, is "agape", there are only two chapters where the agap- and phil- forms appear together with significant contrast or interplay. On this comparison, chapter 21 usually gets all the (erroneous) attention, but less noticed (sadly) is that Chapter 15 had already set up a semantic relationship between phil- and agap- words.
In that chapter, the Friend is the one who Loves, and the one who loves is the friend (v.13,14,15). And while the world loves "like a friend" (15:19), so had the Father loved Jesus "like a friend" (5:20); so had Jesus loved Lazarus (11:3,36); so had Phillip's supplicants been challenged (12:25); and so (once) is called the beloved disciple (20:2). And in John 16:27, Jesus tells Peter and the rest of his disciples "the Father Himself philei you, because you pephilekate me". Thus, if Christian Linguists must think of phileo as "love like a friend loves", they must also admit this type of love gets contextualized with a very High pedigree, in John's Gospel.
So, then what's going on with Peter and Jesus, in chapter 21?
Here's how I put it a couple of years ago:
having breathed in the Holy Spirit and learning to practice the Lord’s presence during His periods of physical absence, Peter was simply itching for some more active type of occupation, besides being just spiritual. [Which is why he went fishing.] So when Jesus sounded like he wanted a favor, Peter sounded eager to please, but then he clammed up at the favor that was requested. Finally, Jesus challenged Peter’s confident claim to be such a friend... if he didn't want to go [where God wanted him to].Jesus' question, "Agapete me?", was an obvious prompt for a favor. Peter's "Yes, Lord, philw" was an affirmative, both times. "You want agape? A friend loves." In other words, Peter was saying, "I'm your man, Lord, what do you need?"
In Peter's mouth, "Phileo" wasn't less than Agape. It was more.
From the upper room to the Sea of Tiberias, Jesus needed his best friends to prepare for a new mission - to love one another, yes, but to do so in Jerusalem; not heading back to their former vocations, not to feed their own families, but to trust God's provision for fish and bread, and to come provide food for God's family.
And so they did. Because that's what Friends do. They Love.
For a more Story-based investigation, incorporating Luke 24:34, and to see how I initially formed this opinion, peruse my series from 2009: