What did the Judaizers want Paul to admit and tell his congregations to do?
The Judaizers wanted Paul to admit he had been wrong and had taught incorrectly, then return to his congregations and tell them to give in. They wanted him to say to practice circumcision, keep the dietary laws, and keep the Laws of Moses.
Les explains that the Judaizers, though most were now believers in Christ as the Messiah, came in secretly to spy out the liberty believers have in Christ Jesus. They wanted to bring Paul back under bondage, which means the Law. They especially watched Paul and Barnabas in relation to Titus, a Gentile, checking whether they practiced circumcision, and they likely watched how they ate, asking if they ate kosher. Their aim was to submarine and sink Paul, to put him out of business rather than let him go to the Gentiles with his message. So they wanted Paul to concede, “Okay fellows, you win,” go back to his congregations, admit he had it all wrong and had taught them wrong, and tell them to give in—to practice circumcision, keep the dietary Laws, and keep the Laws of Moses, because he was supposedly wrong.