1:12 For our boasting is this: the testimony of our conscience that we conducted ourselves in the world in simplicity and godly sincerity, not with fleshly wisdom but by the grace of God, and more abundantly toward you. 13 For we are not writing any other things to you than what you read or understand. Now I trust you will understand, even to the end 14 (as also you have understood us in part), that we are your boast as you also are ours, in the day of the Lord Jesus.
In these few words Paul describes his life mission. He just wants to follow Jesus. In the description he uses two terms in opposition to one another. The first is fleshly wisdom. The second is the grace of God. Basically he is saying in life we have two paths to choose from. The first and most often chosen is the path of human wisdom. We do what seems right to us in the moment. We judge ourselves and others by what we or conventional wisdom deems is right.
Judas followed Jesus physically but in his mind and heart his master was always human wisdom. He was secretly trying to accumulate wealth for himself because human wisdom dictates that this is the best and safest way. In the end he betrayed Jesus and sold Him out because through the eyes of human wisdom he couldn't see how the kingdom Jesus was building would ever stand. Winning by losing makes no sense in the realm of human wisdom. In the end Judas killed himself. Why? Because there is no grace in the kingdom of human wisdom. You do the crime, you do the time. He couldn't live with what he had done but failed to ever see grace and was left with but one option.
Paul has a different story. He too betrayed Jesus by hunting down Christians. He too was blind to the grace of God and was a slave to human wisdom. The difference was that when Paul was personally confronted by Jesus and realized what he had been doing and saw a choice he took it. He abandoned the kingdom of human wisdom for the kingdom of God's grace. Judas had the same choice. He just refused to take it.
Note the results. Paul has a clear conscience now. He knows his past. He knows he can't trust his own heart or his own wisdom. However even with all that being true he has no regrets and no guilt. He sleeps well at night. He lives simply. No need to clamor after everything the world says is valuable. He lives sincerely. Whatever God directs him to do, that he does. If he makes a mistake he just keeps moving forward because he lives in the kingdom of grace.
That's why he can boast of the church in Corinth. He's not proud of them because they are perfect. Human wisdom boasts only in successes. Paul boasts simply because they have chosen the kingdom of grace.
We all face the same choice. There are only two kingdoms.