Paul refers to what he is about to do as foolishness. He then tells the Corinthians about his knowledge and accomplishments. It’s like a résumé. He seems to be embarrassed to sound like he’s bragging about himself, but he just wants them to listen and accept the truths he has taught them.
Telling others why they should listen to you isn’t bragging if what you are trying to convince them of is for their benefit. If your experience or knowledge can help someone avoid a mistake, you may need to tell a story of something you did well. But your stories shouldn’t always be ones where you are the hero; Paul also admitted to being the worst sinner (1 Timothy 1:15).