Paul compares the underage heir to a slave: though owner of everything, he is under guardians until the date set by his father. So also we were enslaved under the elementary principles of the world. But when the fullness of time came, God sent his Son, born of woman, born under the law, to redeem those under the law, so that we might receive adoption as sons. God sent the Spirit of his Son into our hearts, crying Abba, Father. You are no longer a slave but a son, and if a son, then an heir through God.
Paul wonders how the Galatians, who once served those who are not gods, now that God knows them, want to turn back to the weak elementary principles by observing days, months, seasons and years. He fears he has labored in vain.
He addresses them with affection: he asks them to become as he is, for he became as they are. He recalls that he first preached to them because of a bodily illness and that they welcomed him as an angel of God; they would have given him their very eyes. Now he fears he is their enemy for telling the truth. Those who court them do not do so for good. Paul is in labor pains until Christ is formed in them, and he is perplexed.
Finally he illustrates with the story of Abraham, who had one son by the slave woman and another by the free woman. The son of the slave was born according to the flesh; the son of the free woman, through the promise. Paul sees an allegory of two covenants: Hagar corresponds to Mount Sinai and the present Jerusalem, enslaved with her children, and Sarah to the Jerusalem above, free and our mother. Quoting Isaiah, he calls the barren woman to rejoice. Like Isaac, believers are children of the promise; and as the one born according to the flesh persecuted the one born according to the Spirit, so it is now. Scripture says to cast out the slave woman and her son. Believers are not children of the slave but of the free woman.