There are two categories of people known as "children of Abraham." The first are those who claim a fleshly connection by human lineage to Abraham.
Matthew 3:7-9 (HCSB) When he saw many of the Pharisees and Sadducees coming to the place of his baptism, he said to them, “Brood of vipers! Who warned you to flee from the coming wrath? Therefore produce fruit consistent with repentance. And don’t presume to say to yourselves, ‘We have Abraham as our father.’ For I tell you that God is able to raise up children for Abraham from these stones!
The second are those who are claimed by Christ as His own.
Genesis 12:1-3 (ESV) Now the LORD said to Abram, “Go from your country and your kindred and your father’s house to the land that I will show you. And I will make of you a great nation, and I will bless you and make your name great, so that you will be a blessing. I will bless those who bless you, and him who dishonors you I will curse, and in you all the families of the earth shall be blessed.”
Genesis 12:7 (KJV) And the LORD appeared unto Abram, and said, Unto thy seed will I give this land.
Galatians 3:16 (HCSB) Now the promises were spoken to Abraham and to his seed. He does not say “and to seeds,” as though referring to many, but referring to one, and to your seed, who is Christ.
Jesus said that Abraham had rejoiced to see Him, Jesus, in his, Abraham's, day (John 8:56). Abraham was not looking for the promise to be fulfilled in a piece of dirt in what we call the Middle East. Hebrews 11:10 (HCSB) "For he was looking forward to the city that has foundations, whose architect and builder is God." Abraham knew the promise was to be fulfilled spiritually.
Galatians 3:18 (HCSB) "For if the inheritance is from the law, it is no longer from the promise; but God granted it to Abraham through the promise." Jews put much importance on inheritance, the Bible tells much of this. But the better promises upon which the New Covenant is built (Heb 8:6) bring the spiritual reality of reconciliation with God to Abraham's children. Galatians 3:29 (HCSB) And if you belong to Christ, then you are Abraham’s seed, heirs according to the promise.
Galatians 3:6-7 (HCSB) Just as Abraham believed God, and it was credited to him for righteousness, then understand that those who have faith are Abraham’s sons.
Romans 4:13-16 (HCSB) For the promise to Abraham or to his descendants that he would inherit the world was not through the law, but through the righteousness that comes by faith. If those who are of the law are heirs, faith is made empty and the promise is canceled. For the law produces wrath. And where there is no law, there is no transgression. This is why the promise is by faith, so that it may be according to grace, to guarantee it to all the descendants—not only to those who are of the law but also to those who are of Abraham’s faith. He is the father of us all
Hebrews 2:16 (HCSB) For it is clear that He does not reach out to help angels, but to help Abraham’s offspring.
If the atonement was universal, if Christ had died for all men, this passage in Heb 2 would have said that Jesus came to help Adam's offspring. But it says He came to help Abraham's offspring. Not those who merely claim Abraham through physical lineage; those who have faith like Abraham and walk as he walked. He is the father of all who believe. These are the children of Abraham according to promise. And Christ Jesus is the faithful Son into Whose hands all the chosen ones were given.
