What was the false teaching that had come into Paul's churches?
The false teaching was law keeping and circumcision mixed with Paul's Gospel of Grace. It had come into the churches Paul started, and the letter to the Galatians was written primarily to straighten out that error. So the problem was adding law and circumcision to the Gospel of Grace.
Les explains that this little letter, in Galatians chapter 2, was written primarily to straighten out the false teaching that had come into Paul's churches that he had started. That false teaching was law keeping and circumcision, plus Paul's Gospel of Grace. So the problem was a mixture of law keeping and circumcision with Paul's Gospel of Grace.