Children of Promise In Genesis God promised a son to Abraham. Yet Abraham had many sons; so which one was "the son of promise"? (Gen. 25:1-6) It is clear from the narrative that Isaac is the one.
Paul is merely using this story figuratively to show what other early Christian disciples taught: DNA alone (gene pool of Abraham) does not mean Jews are accepted by God in His plan of redemption. Only those approved by God are His spiritual children.
Jesus came to those who were His own (nationality), but His own did not receive Him.
Yet to all who receive Him, to those who believed in His name, He gave the right to become children of God---children born not of natural descent, nor of human decision or a husband's will, but born of God. (John 1:11-13)
Paul used this exclusivity requirement in another epistle of His figuratively:
It is written that Abraham had two sons, one by the slave woman and the other by the free woman. His son by the slave woman was born in the ordinary way; but the son by the free woman was born as the result of a promise.
These things may be taken figuratively, for the women represent two covenants...
Now you brothers, like Isaac, are children of promise. (Galatians 4:22-28)
The Apostle Paul is just using figures of speech to show that only those who believe the Gospel of Grace are redeemed, and children of God. Those who wish to observe the rites and regulations of the Mosaic Law as a way to be accepted by God, are on a fool's errand. By the works of the flesh no man can be justified.
The Law was instituted as a schoolmaster to bring us to Christ*. But now that Christ has provided a way to heaven by His sacrificial death (Lamb of God), no other way is needed...or accepted. (Gal. 3:24) The Law and the Prophets were until John. Since that time, the Good News of the Kingdom of God is evangelized (Luke 16:16)
Isaac represents the disciples of Christ in all countries who accept Jesus and put faith in Him alone for salvation. Thus fulfilling the promise to Abraham that through His Seed, not just the Jewish race, but the whole world would be blessed! All the nations come to a saving knowledge by grace. (ethnics, Gk.)
Addendum Some are concerned about what skeptics call the Replacement Theory. As if some teach that the Jewish way of life has been set side for a different ethnic one.
It is true that God Himself has instituted a New Covenant. (Jeremiah 31:31, Hebrews 8:7-13) The old one is obsolete. The sacrifices according to the Mosaic Law have been discontinued because of the Lamb of God's eternal sacrifice. The office of the Aaronic high priest is no longer in effect because of Jesus in the order of the Melchizedek priesthood. (Hebrews 7)
All these have definitely been replaced. And importantly, being chosen people simply because of Semitic DNA in one's gene pool, is no longer true---if ever it was, because God has always required a circumcised heart. But, having recognized this, it is also true that a person of Jewish birth is most welcome into the community of believers with joy, realizing that much of the Old was type and shadows of the New, in which he now belongs with a greater spiritual meaning and reality!
The modern Church is NOT a Gentile replacement; it is the amalgamation of sin-freed ethnics bonded together with sin-freed Jews! One New Body (Man), neither characterized as Gentile, nor as Jewish...but as blood-washed, born-again, heaven-bound, saints of God!