What was Paul's confidence about the carnal church at Corinth?

Paul had genuine confidence that the carnal church at Corinth could grow and become real trophies of God’s grace, in spite of all the pressure. He also expressed confidence in them, saying his joy was the joy of them all.

Les explains that verse 4 says Paul had “confidence in you, that my joy is the joy of you all.” Paul’s whole mental concept concerning this carnal church at Corinth was that they could grow and become real trophies of God’s grace, in spite of all the pressure. Les reminds us that these early Christians, the moment they professed faith in Christ, were under pressure from the Jewish element and the pagan element, and only a precious few were won out. Paul wrote out of much affliction and anguish of heart, with many tears, and his heart was broken over what he heard from the congregation at Corinth, yet he still held confidence that they could grow.

2 Corinthians 2:3

And I wrote this same unto you, lest, when I came, I should have sorrow from them of whom I ought to rejoice; having confidence in you all, that my joy is the joy of you all.

Why did Paul write to the Corinthians so that he wouldn't have sorrow when he came?

Paul wrote to the Corinthians so that, when he came, he would not have sorrow or grief from those who should have brought him joy. He did not want to hear things in the church that made him sorry instead of joyful.