What does 2 Corinthians 13:10 mean?
Before turning to his closing words, Paul sums up the purpose for this letter to the church in Corinth. He has written everything for their good and to build them up, not to tear them down. More urgently, he seeks to convince them to repent of sin before he arrives. That way, he will not need to be severe in judging and disciplining those who remain unrepentant of ongoing sinful choices (2 Corinthians 12:19—13:2).Despite charges against him by false apostles and other critics, Paul asserts once more that he is a true apostle, given valid authority to act on Christ's behalf when he is with them. He warned that, acting on this authority, he will spare no one who is still following sinful ways when he arrives (2 Corinthians 13:2). They will see that, in Christ, Paul can be as strident as necessary to hold them accountable for betraying their devotion to Christ. This, as well, is meant for their good. Even if severe discipline is required, Paul makes clear his purpose will not be to dole out ruin and misery. As God does for all who are in Christ, Paul will only act to benefit them, even if that requires some temporary pain.
It's also very clear that Paul does not want a severe confrontation with the believers of Corinth. It's not something he wants to be forced into. He truly hopes that all will repent so their time together can be pleasant for everyone.