What does 2 Corinthians 10:15 mean?
Paul wrote in the previous verses that he refuses to participate in a popularity competition with his opponents in Corinth. He's not interested in scrabbling to be seen as the most impressive speaker or the best at self-promotion. These false teachers were competing according to the world's standards of comparison and measuring themselves against each other.The mission given and empowered by God did not require Paul to prove himself worthy. He didn't need to worry about putting on a show, giving impressive performances. Also, Paul had already completed the task at hand. He had reached the Corinthians with the gospel of Jesus, and they had believed. That's all he had set out to do.
Paul adds now that he does not boast in work accomplished by others. He may mean that his opponents, the false teachers in Corinth, are attempting to claim the Corinthians as their own. This was despite the fact that Paul was the one who established the church there. He is the one who introduced the Corinthians to Christ, something they knew well.
Though the main task has been attained, Paul does not see his work as finished. His words here do not mean he has nothing left to do, now that those in the church in Corinth have come to Christ. Paul's hope is that as their faith grows, his influence for Christ among them will grow, as well. This may mean that he hopes to see more and more people come to faith in Christ or that he hopes that they will contribute to his ministry so that he can replicate in other places what he has accomplished, in God's power, among them.