Paul had written a harsh letter to the Corinthians, but in person he had apparently been gentler in his approach. He makes it clear that his harshness was not a result of pride, but an obligation to correct them as a spiritual leader. What he did was for God’s sake, not his own.
All Christians carry some level of spiritual responsibility for others. For some it’s defined by a role like a pastor, elder or parent. For all of us, we have a responsibility to be watching out for each other. Sometimes it’s to correct; other times it’s to encourage. It should always be motivated by a desire to bring the other person closer to God and never selfishly motivated.