The question presented in chapters 9, 10, and 11 is Can God be trusted to do what He says? The issue is that we have read such wonderful things in chapter 8, and now Paul is presuming a challenge to this, based on a misunderstanding around Israel's position. Verses 1-5 introduced the idea, and now Paul begins his train of thought.
We, as believers, need to have absolute trust in God to accomplish what He has promised. This is fundamental to our security as believers. God combines the power to fulfil all His promises and is trustworthy to do so!
We have to study the past - the Old Testament - to see how the story of Israel provides the answers to God's fulfilment of His promises, so that we may now believe in those promises made in chapter 8.
In verse 6 we are introduced to a concept of a sub-group within Israel. An Israel within Israel. These 2 Israels include physical Israel and spiritual Israel. Think of an egg. Both the white and the yoke are the egg (physical Israel), however, the yoke is separate (spiritual Israel), yet part of the egg. In Galatians 6:15-16, we are introduced to the yoke, or this spiritual Israel as the Israel of God:
Neither circumcision nor uncircumcision means anything; what counts is the new creation. Peace and mercy to all who follow this rule—to the Israel of God. (Galatians 6:15-16)
The concept is that not all Jews by birth belong to the Israel of God (aka The Church). Paul now leans on Abraham again (as he did in the earlier chapters of Romans to show that we are justified by faith, not by works). This time we see how the seed of Israel is passed down, not by normal inheritance protocol, by through the child of promise.
If you are unfamiliar with the Abraham and Sarah story and the births of Ishmael and Isaac, read Genesis chapters 16 and 21. Paul nicely summaries the difference between Ishmael and Isaac in Galatians 4:28-29:
Now you, brothers and sisters, like Isaac, are children of promise. At that time the son born according to the flesh persecuted the son born by the power of the Spirit. It is the same now.
Isaac was the descendant, the child, that God had promised and is, therefore, the child of promise, the name now given to believers, followers of Christ, Israel of God. Ishmael on the other hand is the son born first, of flesh. The child conceived despite God's promise. Ishmael was older, however, God selected Isaac to be the offspring promised in the covenant with Abraham. Ishmael represents the believer’s first birth (the flesh) and Isaac represents the second birth (the Spirit). When, like Isaac, you are born of the Spirit, you are born rich (Genesis 21:10). Isaac was the heir of all that his father owned, and God’s children are “heirs of God, and joint-heirs with Christ” (Romans 8:17).
But God said to him, “Do not be so distressed about the boy and your slave woman. Listen to whatever Sarah tells you, because it is through Isaac that your offspring will be reckoned. (Genesis 21:12)
We see then that the promise is not based on birth order, but rather the intervention of the sovereign God. Isaac, who was conceived through the miracle of God's actions and not through their own doing.
We could argue that Isaac and Ishmael came from different mothers, so this could result in the intervention observed, but not so in Paul's second example. This time Isaac's sons. Isaac and Rebekah (his wife) conceived twins. The same single act of conception. Jacob and Esau. Jacob was the younger of the two twins, yet even before they were born, Rebekah was told by the LORD, "the older will serve the younger" (Genesis 25:23). This shows God's choice to intervene. To reverse the natural order of birth rights.
These two examples show God's purpose in election. The word 'election' comes from the same root word for 'to call'. It is through Him (God) that Jacob's status changed. It is not by chance and it is not an invitation. Paul then quotes Malachi 1:2-3, which links to God loving Jacob (Israel) and hating Esau (Edom). Paul's reference here is unlikely to speak to the physical nations of old, but rather the very personal calling we each receive. Jacob, like Isaac before him, and us who follow after, are the Israel of God.
We are talking election here, and we can often get distracted by the various ideas and theological positions surrounding Soteriology. The idea that we do nothing, that even our faith is under sovereign rule, (Calvinist), which is that salvation is through unconditional election. While Arminianists see salvation as being based on God foreseeing our faith.
I see true Christians, those under the banner of Israel of God, on a plane - assured of our destination. The Calvinist view is that God purchased the ticket for us and we had no alternative but to be on that plane. Arminianists see us on the same plane, but we have purchased the ticket ourselves, however, God did know we were going to buy the ticket.
How do we see God's power, the power and the love of His grace?
We like to think of things as binary, black or white. In God's infinite wisdom all things may be possible and therefore these are nice frameworks and discussion points, but they are not meant to divide, rather show us how blessed we are that we have no condemnation through Christ, and we can not be separated from His great love - ever!