Paul moves rapidly from defensive posture to poetical praise. He is in his heart besotted with the believers in Corinth. It may not have been obvious from reading some of his words before this, but he rejoices in them and feels proud of them.
In the ancient world there was a custom of sending letters of commendation with a person, introducing them and testifying to their character. We still have a near equivalent when someone applies for a job and is asked to provide references including a character reference. If you have the opportunity to look at Romans chapter 16 v 1 and 2, we have an example as Paul commends Phoebe, a deacon in the church in Cenchrea, to the church in Rome.
It was legendary also in the ancient world that Christians could be easily duped, so willing were they to see the good in someone and embrace them as a friend. That may well be why the salutary tale of Ananias and Sapphira is there in Acts chapter 5.
Previously it may have appeared that Paul was writing his own testimony, but he recognised that others-probably ultra orthodox Jews-had penetrated Christian fellowships with letters of commendation and then had worked hard to spoil Paul's work and to discredit his apostolic authority. Paul had possibly used such letters himself before his conversion when he journeyed to destroy the nascent church, but now he declares that his only commendation comes from the Corinthian believers. Every one of them is a letter of Christ in their transformed hearts and lives. Plato had commented long before Paul's letters that the good teacher does not write his message in ink that will fade; he writes it upon his pupils, men and women. My greatest joy is witnessing those I love growing closer to Jesus daily: you give me so much joy through your lives! Jesus had written His message on the Corinthians with the Spirit: not on tablets of stone as the Ten Commandments, but on the hearts of people!
When we ran our shop, we would often hear criticisms about the other shopkeepers in the village. One of them was that some cheated on weighing out what they were selling. Every Christian is an advertisement for Christianity, the world has always judged Jesus Christ by His followers.