VERSES 22, 23. For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman. But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.
This is Paul's allegory. Abraham had two sons: Ishmael by Hagar, and Isaac by Sarah. They were both the true sons of Abraham, with this difference, that Ishmael was born after the flesh, i.e., without the commandment and promise of God, while Isaac was born according to the promise.
With the permission of Sarah, Abraham took Hagar, Sarah's bondwoman, to wife. Sarah knew that God had promised to make her husband Abraham the father of a nation, and she hoped that she would be the mother of this promised nation. But with the passage of the years her hope died out. In order that the promise of God should not be annulled by her barrenness this holy woman resigned her right and honor to her maid. This was no easy thing for her to do. She abased herself. She thought: "God is no liar. What He has promised He will perform. But perhaps God does not want me to be the mother of Abraham's posterity. Perhaps He prefers Hagar for the honor."
Ishmael was thus born without a special word or promise of God, at the mere request of Sarah. God did not command Abraham to take Hagar, nor did God promise to bless the coalition. It is evident that Ishmael was the son of Abraham after the flesh, and not after the promise.
In the ninth chapter of the Epistle to the Romans St. Paul advances the same argument which he amplifies into an allegory in writing to the Galatians. There he argues that all the children of Abraham are not the children of God. For Abraham had two kinds of children, children born of the promise, like Isaac, and other children born without the promise, as Ishmael. With this argument Paul squelched the proud Jews who gloried that they were the children of God because they were the seed and the children of Abraham. Paul makes it clear enough that it takes more than an Abrahamic pedigree to be a child of God. To be a child of God requires faith in Christ.