The Galatian church is being tempted to return to their old ways, following the Law of Moses rather than putting their trust in Jesus. Paul has some very unkind and unflattering things to say about those who are leading the Galatians back to their old ways, and also some hard questions for the Galatians themselves.
Paul likens them to the mothers of Abraham’s two sons, Isaac and Ishmael. If you remember, Sarah, Abraham’s wife, was barren yet God had promised him a son. So together they decide that Abraham should conceive a child through Sarah’s servant, Hagar. He does so and Ishmael is born. But this is not God’s plan but Abraham and Sarah’s. Later, Sarah is miraculously given a child of her own, Isaac, to fulfill God’s promise to them. As the boys grow, Sarah fears that Ishmael, as the older of the two, will take the inheritance from Isaac, so she tells Abraham to banish Hagar and Ishmael to the desert, which he does. They almost starve to death until God intervenes and saves them.
Paul uses these two to identify the two ways of life – life under the old regime of the OT Law, and life under the new regime of Christ’s death and resurrection. The old way is the way of slavery, for Hagar was a slave woman. The new way is the way of freedom, for Sarah was Abraham’s free wife. The old way is the way of the flesh, for Ishmael was the human plan. The new way is the way of divine purpose, for Isaac was God’s plan. The old way is the way of persecuting those of the new way, as Ishmael persecuted his brother.
All of this is to say that following Christ is God’s plan, is freedom, and yet will be persecuted by the Jews. It is the way Paul taught, and any other way is heresy, slavery, and simply our own design, not God’s.