With these words, Paul is reminding the Galatians that those who seek to earn God’s favour through obedience to old covenant law will not receive the promised inheritance. The son of the slave will not share in the inheritance with the son of promise. He is not encouraging them to expel the Judaizers, though that would be a natural application to draw from these words.1
30 But what does the Scripture say? “Cast out the slave woman and her son, for the son of the slave woman shall not inherit with the son of the free woman.”