Observation: As Paul is talking to the church about his qualifications to correct them, he wants to make the point that - in fact - earthly qualifications are pointless. Within the church, we may correct each other only by understanding the word of the Lord and the instructions of Jesus, and aligning correction to those truths. However, since the church at Corinth seems to push back on worldly qualifications, Paul will prove is worthiness.
That said, Paul mocks them a little before doing so, pointing out that his words are foolish, yet ... they like to suffer fools, because they themselves are so wise! If they knew themselves to be fools, then they would want to listen to good and wise instruction and correction. However, since they don't want to listen, then they certainly consider themselves wise, and in being wise they know well enough to 'suffer fools' and let them ramble.
It is all an elegant trap to show the church they are failing to listen and learn and grow. If they were fools, they of course would want wisdom, and that being the wisdom of the very word of God. Since they reject wisdom, then of course they will listen to foolish boasts, and that being the boasts about worldly qualifications of wisdom ... qualifications which exceed any of them.
Application: I have done this before at work, in various forms, used certain "worldly" concepts that some people think are important to learn what drives or motivates or incents them that is not necessarily accurate or true. It is a way of determining if people have the right priorities, and in Paul's case the "right priority" when it comes to wisdom and truth is the word of God inspired by the Holy Spirit, not earthly credentials.
What I like best, though, is the way Paul 'traps' the audience into listening to him. If they are so wise ... then they can easily listen to a fool! This is becoming more and more an issue in modern society, as we see people who engage in public debate on social topics who declare their wisdom and knowledge about certain "truths" but then cannot and will not listen to people they call 'idiots' or 'fools' or worse. We see videos of believers on the front line engaging in debates, and the other side won't debate, they will only yell and spout soundbites out of context then walk away while calling others names.
And once again ... we see that isn't a new thing. Paul faced that kind of behavior 1,900 years ago, and showed a calm way of calling it out.
Prayer: Lord, again today I find myself to be a total fool. However, I do want to listen to correction. Please forgive my sins and correct my mind, help me readjust my thinking, and give me the tools I need to focus on you every minute of every day. I am failing at this, and I know I am not wise enough to solve it myself. Amen.