Paul talks a great deal about “boasting.” Boasting for Paul though usually entails a sense of self-reliance before God, not a braggadocious spiritual arrogance. When Paul boasts, then, he wants to boast in the things that honor God and not himself.
Paul is not concerned about looking good. He loves to make God look good. So he boasts in God at the one place where Paul’s sin and need look the worst and God’s goodness looks the best: the cross.