Peter was hurt because Jesus asked him the third time, "Do you love me?"
It's not about us. Peter had just experienced three incredible years with Jesus, but they culminated in a colossal failure. After a marketplace miracle that demonstrated Christ's authority and awesomeness, Jesus got Peter back to basics. “Feed my lambs. Take care of my sheep. Feed my sheep.” In the midst of this, Peter has a pity party. “Peter was hurt...” The way Jesus counters his introspection is by resetting the context. It's as if Jesus is saying, ‘This is not about how you feel, Peter, but it is about life and death, darkness versus light, the future of the Church. Get over how you feel.’
When you get in the trenches with others doing kingdom business, there is potential for hurt. Let's relinquish our “right” to self-pity, our mandate to mope, and subjugate it to the broader agenda of God's business. “But I don't feel like working with... But I felt ignored... But this isn't my gifting... And I failed last week...”
Jesus points Peter to the end of his life:
When you are old you will stretch out your hands and someone else will dress you and lead you where you do not want to go. Jesus said this to indicate the kind of death by which He would glorify God.
Want context? One day we will die. It is not about us; it is about following Jesus and doing the job he gives us to do. “Then He said to him, ‘Follow Me!’”