I stated in the video that in verses 6b – 7 Paul is beginning to use an allegory. When he says in 7, “nor are they children because they are Abraham’s descendants, but; through Isaac your descendants will be named,” he is introducing the story about how the nation of Israel was established according to a promise (which he expounds upon in verses 9-13) in order to make a point about how the Israel of God is also established according to a promise.
Why would we think that the establishment of the nation of Israel would be used in an allegorical sense to speak about the establishment of the Israel of God? Well Paul uses and defines this allegory in one of His of letters – Galatians.
He says in Galatians 4:23 that Abraham had two sons (Ismael and Isaac), and that the one born according to the bondwoman (Ismael being born to Hagar) was born according to the flesh and the one was born according to a free woman (Isaac to Sarah) was born according to a promise.
He goes on to say in verse 24 that says that allegorically speaking these two women represent two covenants:
Ismael born to Hagar – Hagar allegorically represents the “present day Jerusalem” which is in slavery. This would be the physical nation of Israel – those who were born Israelites according to the flesh (genetically) but as Jesus says in John 8 were still slaves to sin and had not yet been set free by the Son.
Isaac born to Sarah – Sarah allegorically represents the free Jerusalem. Paul refers to those in the church as the children of promise in verse 28 and a part of the free Jerusalem. Those who are apart of the “free Jerusalem” are those who are born according to the Spirit (Gal 4:29).
If Paul says here in Galatians that Isaac being born to Sarah is meant to allegorically represent those who are born to the free Jerusalem/Israel of God/the church, it would make sense for Paul to use this same allegory and in Romans 9 to make a point about who the true children of God are.