I think we assume we would recognise false teaching immediately when we heard it, but Paul needed to tell the Galatians: this teaching you’ve been persuaded by is not from God. False teachers don’t advertise themselves as false teachers, so we need to listen carefully to see whether what we’re hearing is in line with the gospel of the grace of Jesus Christ or not.
The preacher might seem like a really sincere Christian, but if he’s teaching you to rely on your performance in addition to Christ’s, then he’s not speaking on behalf of God.
These people in Galatia were using the Old Testament law in their teaching. Just because someone quotes from the Bible, doesn’t necessarily mean they’re presenting God’s message faithfully.
Paul says God calls you to freedom (v13: “you were called to freedom brothers”). This preacher is calling you to slavery to the law. Of course he doesn’t call it that; he calls it faithful Christian living, but if you follow him, you’ll fall away from grace (v4). Don’t be persuaded to start trying to earn your acceptance with God, because that persuasion doesn’t come from God.