What does Galatians 3:7 mean?

A group known as the Judaizers are attempting to promote a works-based version of Christianity (Galatians 2:4). According to these false teachers, salvation only starts with believing in Jesus, but then one must be circumcised and follow the rituals of the law in order to be truly saved and accepted by God. Paul's reason for writing to the Galatians was to tell them that this teaching was false (Galatians 1:6–9). These false teachers insisted that nobody could be included in the family of God unless they were descendants of Abraham. By that logic, if non-Jews, like Paul's readers in Galatia, wanted to be in God's family, they must do what all Jewish men do. They must be circumcised (Genesis 17:10). Paul, however, has just pointed out that God called Abraham righteous long before he was circumcised. Paul has quoted Genesis 15:6: "And he believed the Lord, and he counted it to him as righteousness."

Now, Paul declares a radical idea: everyone who believes the Lord, referred to as "those of faith," are the sons of Abraham. This includes all people, even the non-Jewish people known as Gentiles. This is a point Paul will make explicitly clear at the end of this passage (Galatians 3:23–29).

In other words, Father Abraham's "many sons" include all who trust in Christ. This category is not limited to those descended from Abraham by birth and through a ritual conversion to Judaism. Resistance to this truth caused much of the persecution of Christians by the Jewish religious leaders in the early years of church.