There are two main themes in this chapter of Galatians.
1—being a child of Abraham through Faith
For Paul, faith = belief in the crucified and risen Jesus Christ, and so when he speaks of faith “coming” (v. 23) he refers to the “era of Christ” as a particular time marked by Christ’s death and resurrection. It is through this relationship of faith, through Christ, that believers receive the Spirit (v. 2) and are saved, reconciled to God.
A portion of this chapter tries to explain how Abraham, who lived prior to Christ, of course, could be the father of the faith, if “faith” hadn’t come yet. Paul cites several examples from Hebrew scripture of how God was working through Abraham and the law to prepare people for faith, when Christ would come. But he is careful to remind it was not the law that saved anyone, ever—then or now. Rather, it is faith in Christ Jesus.
Being a “child of Abraham” (v. 7) means we believe in the same gospel, the same Lord, the same work God is doing, work which began long before Christ but was revealed in Christ as faith, and continues through the Spirit. Theologically we agree with this: those who believe in Jesus are one “family”. Being a child of Abraham is not a genealogical reality, it is about faith. While there are many stories in the New Testament about entire households being baptized once the head of the house believed in Jesus, making baptism a family thing, Paul’s point is that heritage doesn’t matter, faith does. Remember, he’s arguing against those who insist Gentiles must become Jewish before being Christian.)
2—identity as a child of God
Paul redefines this new identity in faith. One of the purposes of the law was to form a common identity among the people of God. Sort of like we might sing “They’ll know we are Christians by our love”, in Hebrew scripture they knew they were Jewish because they followed the Mosaic law. But now Paul proclaims a new source for identity: baptism into Christ (v. 27). Who you used to be (Jew or Gentile, slave or free, male or female) doesn’t matter as much as who you are now: child of God. The things that used to mark people as different from one another give way to a common identity in Christ. One is not better than another; all are beloved children in God’s eyes.
Finally Paul closes the circle of this argument and proclaims that all who are made new in Christ Jesus, all who are baptized and have put on Christ, all who share this identity, are Abraham’s offspring. It is that key relationship of faith, a gift from the Holy Spirit, that holds all of these pieces together. Whether Jew (following the Law) or Gentile, slave or free, male or female—all these differences come together to form the people of God, rooted in Abraham, and united in Jesus.
Throughout this epistle, Paul does a nice job of showing the importance of the Law and his own respect for it, while insisting that the law is not what saves us. Now he has brought Abraham into the argument, not just “the law” in a theoretical way, but an example to whom they can relate, to show how God’s grace works not only on a timeline (as if the ancestors are out of luck because they lived before Jesus) but eternally in both directions.