That's a bit odd, since Jesus keeps repeating himself until he and Petera are talking about the same thing:Not to burst the bubble here ... but most solid Greek scholars believe the different uses of love in John 21 is irrelevant. There is no reason to believe it has any significance.
J - Peter do you love me completely (agape)?
P - I love you like a brother (phileo).
J - Peter do you love me completely (agape)?
P - I love you like a brother (phileo).
J - Peter do you love me like a brother (phileo)?
P - You know I love you like a brother (phileo)!
You can't read this passage in the Greek and not see the significance on the two separate words, whose distinct meaning is lost in the English. There are many places where the words can be contextually interchanged. But this is not one of them. There's a reason Jesus and Peter are using different words here. We need to understand why they are doing so. We cannot understand this without looking at the source texts.