Why does Paul think all descendants of Abraham are Israel? ~ Cross reference of Romans 9:7 to Genesis 21:12,Genesis 18:10, Genesis 18:14

G-d made a promise to Abraham that his descendants will posses the land of Cannan and that G-d will multiply his seed. G-d later makes the same promise to Isaac that through his see the promise made to Abraham will be fulfilled. Finally G-d makes the same promise to Jacob that his name is Israel and his 12 sons will be blessed and the promise G-d made to Abraham, Isaac & Jacob will be fulfilled in them.

So Paul stating that all dependents of Abraham are not Israel is correct. Ishmael, other sons through Ketura[Zimran, Jokshan, Medan, Midian, Jishbak, Shuah] & Esau[Isaacs's first born] are not Israel. As you go through the rest of Romans 9 you will see that Paul is using this statement that "All children of Abraham are not Israel, but the ones that came through faith [Isaac]" to later say that through faith the gentiles [Christians] by faith in the blood of Jesus are also Israel. 

Click to read how G-d established his covenant with Abraham to be called his decedents.

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All Greek Text references are from NIV and Tanakh references are from Chabad.

This post is not intended to offend anyone's faith but for those people who are Seeking the truth of THE ONE TRUE G-D of the universe to who we owe all our love, gratitude & devotion.

My encouragement to you is that you read the whole chapter of Tanakh that the Greek text quotes so you get the context and understand what G-d actually said.

G-d Bless and Seek THE Truth.

Romans 9:6 It is not as though God’s word had failed. For not all who are descended from Israel are Israel. 7 Nor because they are his descendants are they all Abraham’s children. On the contrary, “It is through Isaac that your offspring will be reckoned.”[b] 8 In other words, it is not the children by physical descent who are God’s children, but it is the children of the promise who are regarded as Abraham’s offspring. 9 For this was how the promise was stated: “At the appointed time I will return, and Sarah will have a son.”[c]

Genesis 21:12 And God said to Abraham, "Be not displeased concerning the lad and concerning your handmaid; whatever Sarah tells you, hearken to her voice, for in Isaac will be called your seed.

Genesis 18:10 And he said, "I will surely return to you at this time next year, and behold, your wife Sarah will have a son." And Sarah heard from the entrance of the tent, and it was behind him. 

Genesis 18:14 Is anything hidden from the Lord? At the appointed time, I will return to you, at this time next year and Sarah will have a son."

• Yes it is true that G-d promised Abraham that from his seed Isaac and not from Ishmael that his promise will be fulfilled
• Ishmael was blessed just as G-d promised Abraham and you can read an account of his 12 sons in Genesis 25:12-18. This promise still stands today in that the 2nd largest people are the dependents of Ishmael.
• Isaac has 2 sons, but G-d blesses Jacob who becomes the promised blessing Israel. 
• G-d blesses Esau as well and you can see the account of his blessings in Genesis 36 where he becomes the Edom. They fought against Israel and this lasted as long as David's reign. Some say this race migrated out to Europe and merged into the Greco Roman world. 
• So Paul trying to say that Isaac is the promise is right to some extent but the final promise was to Jacob.
• Remember all these are descendent of Abraham and the covenant with them and G-d is circumcision.
• G-d was clear that his promise would be through Abraham, Isaac & Jacob.