What does 2 Corinthians 6:11 mean?

Paul expresses great emotion and affection in this and the following verses. He acknowledges that he has spoken freely to them. In other words, he has not held anything back in order to spare their feelings. As he has made clear, the stakes are too high to be more concerned with gentleness than with truth. Any among them who do not trust in Christ alone for the forgiveness of their sins are in danger of missing the grace of God (2 Corinthians 6:1).

Paul has also spoken freely in defense of his own integrity and authority as an apostle, as well as the integrity of all who minister with them. He has been very clear that there is nothing that he and his co-workers for Christ have done that can legitimately be described as standing in the way of any person trusting in Christ.

Still, despite any conflict with the Christians in Corinth, Paul and his associates' hearts are wide open. As described here, their affection for the Corinthians is as full and deep as it has ever been. In short, Paul loves them as much as he ever has. The fact that he calls them by name, Corinthians, may be evidence of his great affection for them.