Romans 9:6-8 meaning

Paul is writing the letter to the Roman Christians to combat certain competing Jewish "authorities" in Rome who are trying to drag the believers back to following the Jewish Law as a pathway to righteousness. 

We will see in Chapter 16 that Paul's "team" in Rome includes Priscilla and Aquila, a husband-wife team that he preached the gospel alongside during his missionary travels (Romans 16:3). It seems probable that Priscilla and Aquila sent to Paul to ask for his aid, resulting in this epistle.

As Paul has made clear throughout Romans, God is never to blame for man's actions. God cannot be blamed for Israel falling away from Him: But it is not as though the word of God has failed (v 6). 

His promises have not failed. It is how we respond to what God offers us that affects our lives. Many Israelites do not bear a "family resemblance" even though they are descended from Abraham; they do not behave as Abraham did, who was a great man of faith: For they are not all Israel who are descended from Israel; nor are they all children because they are Abraham's descendants (vv 6-7). 

Abraham is the father of those who believe (Romans 4:16). The Jews that rejected Christ failed to follow Abraham's example. They pursued righteousness through the Law, which inevitably leads to putting us under sin. Rather than pursuing faith in God, which leads to true righteousness, they tried the futile objective of gaining righteousness through the Law (Romans 9:30-32).

Israel at its highest spiritual level is not only a nation or race. It is a spiritual family made up of those who believe (Romans 4:16). 

Israel, as we can see from the list of descriptions in Romans 9:4, is supposed to be the example on earth that God uses to show people what living is supposed to be like, how we ought to live. Israel is supposed to be the holy nation, the example that everybody can see. And God put Israel in the cross-section of the world. The primary trade routes went through Israel so people could see, "This is how I want you to live." By Israel's example, all the world could be blessed. That was their assignment, to be a priestly nation (Exodus 19:6). But it isn't happening.

The people of Israel abandoned faith in God and followed the Law as a means of righteousness. They sought to justify themselves, rather than trusting in God. Their leaders rejected their own Savior when He lived among them in the flesh: That is, it is not children of the flesh (biological descendants) who are children of God, but the children of the promise are regarded as descendants (v 8). 

The spiritual descendants of Abraham are those who live by faith. It is not so much the children of the flesh who are Abraham's offspring. Rather, it is those who believe God. It is those who are of faith that are like children of the promise. 

Simply being physically born into the nation of Israel does not mean a person is spiritually a child of God, but living as a person of faith, a spiritual descendant from Abraham (made righteous through his faith), is what being a child of God looks like (Romans 8:30). This is what Paul is referencing when he quotes Genesis here, "Through Isaac your descendants will be named" (v 8).

Abraham had two sons, Ishmael and Isaac. Isaac was the child of promise, therefore it was through him that God told Abraham his descendants will be named. In like manner, the children of promise will be those who live by faith. That applies to all humans. Although Israel has a very special place, God's blessing will not be limited to biological (of the flesh) descendants. Rather, God's blessing will be bestowed upon those who are of faith. Those who follow the faith example of Abraham (Genesis 15:6; Romans 4:3). 

Jesus Himself has a lengthy argument with Israelites about heritage (John 8:37-59). In the debate, the crowd claims they are children of Abraham and children of God, and Jesus tells them if they really were children of God, they would love the Son of God: Jesus. Instead, they are behaving as if their father were Satan (John 8:43-44). 

These Israelites had the literal Son of God standing in front them, and rather than embracing Jesus, they hated Him. At the end of John 8, they tried to stone Him. Those who are of God are those who believe His word and His promises. 

Throughout the Old and New Testament God reaches out to His people. When Christ came as the ultimate figure of divine intervention, Israel rejected Him. However, God has not rejected His people.