"To understand Romans 9, one must start at the beginning.
Paul is writing this book to the Church in Rome, which consists of Jews and Gentiles. The first 8 chapters are as close as we come in the New Testament to a theological treatise of man, sin, soteriology, and Christology. We might include some pneumatology, too. So, Paul's intent for the book is to be very instructional.
Chapter 9 turns a corner as Paul addresses a new topic:
9:1 "I am speaking the truth in Christ—I am not lying; my conscience bears me witness in the Holy Spirit— 2 that I have great sorrow and unceasing anguish in my heart. 3 For I could wish that I myself were accursed and cut off from Christ for the sake of my brothers,[a] my kinsmen according to the flesh."
Paul does not include things in his letters frivolously. Certainly these are Paul's feelings, but there is a greater purpose, here, too. Paul wants to be sure that we know that he is talking specifically about the Jews. We can see this at the end of verse 3, where Paul refers to them as "my kinsmen according to the flesh." The nation of Israel, formed by the Old Covenant on Sinai, is Paul's subject, here.
"4 They are Israelites, and to them belong the adoption, the glory, the covenants, the giving of the law, the worship, and the promises. 5 To them belong the patriarchs, and from their race, according to the flesh, is the Christ, who is God over all, blessed forever. Amen."
And, again, Paul affirms to use that we are talking about the Israelites, and lists 8 things specific to the nation of Israel. And this list of things combined with the fact that they continue to cling to the Old Covanent, and do not come into the New Covenant promises to them (Jer 31) should cause us a bit of dissonance.
And apparently it did just that either for Paul or some of his readers:
"6 But it is not as though the word of God has failed."
OK, major charge being defended, here. Paul is putting a stake in the ground that the fact that Israel (as a whole) isn't coming into the New Covenant does not mean that God's word has failed.
What do we mean by "God's word failed?" Go back to verses 4 and 5. All of the things listed there should point to the nation of Israel, the one formed by the covenant on Mount Sinai when Moses was there, coming into the promised New Covenant established by Christ, and they aren't. And apparently the charge was made about whether God's word failed.
And Paul says that it has not, and the remainders of Romans 9-11 is a defense of that statement.
So, what we see so far is that Paul is speaking about the word of God as it relates to His interaction with the nation of Israel.
For not all who are descended from Israel belong to Israel,
"7 and not all are children of Abraham because they are his offspring, but “Through Isaac shall your offspring be named.” 8 This means that it is not the children of the flesh who are the children of God, but the children of the promise are counted as offspring."
And Paul begins his defense by asserting that there is a subgroup within the nation of Israel, who are his offspring, but are the true Israel because they are children of the promise, not just children by birth.
"9 For this is what the promise said: “About this time next year I will return, and Sarah shall have a son.”
If we recall this story, Sarah gave her servant girl to Abraham for her to bear a child, and Ismael was born. And being the oldest, he would be the natural inheritor. But God makes this promise to Abraham, and Isaac is born, making him the child of the promise.
"10 And not only so, but also when Rebekah had conceived children by one man, our forefather Isaac, 11 though they were not yet born and had done nothing either good or bad—in order that God's purpose of election might continue, not because of works but because of him who calls— 12 she was told, “The older will serve the younger.” 13 As it is written, “Jacob I loved, but Esau I hated.”
And, again, with Isaac, Esau was born first, yet God chose Jacob. In both cases, the elder child who should have received the covenant and promises, but did not. And this happened because it was God's purpose in election: The older will serve the younger. Jacob was selected before he was born, Isaac the promised inheritor before he was conceived.
And this becomes the analogy by which Paul begins to explain promises made to Israel. This sub-group within Israel, those who believed and entered the New Covenant are akin to Isaac and Jacob, and the nation of Israel who did not believe and remained in the Old Covenant are likened to Ishmael and Esau.
"14 What shall we say then? Is there injustice on God's part? By no means! 15 For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” 16 So then it depends not on human will or exertion, but on God, who has mercy."
Note, here, that Paul cites Exodus, just after Israel breaks its covenant, and God threatens to destroy Israel (and changes His mind after Moses refuses to go along with God's plan). After this Moses and God meet at the tent of meeting, and this isn't given as a comfort to Israel, but as a warning that God will keep His own counsel as to whom He extends mercy and compassion.
So, now we have New Covenant Jews who are the "younger", and Old Covenant Jews who are the "older", and God saying that it is up to Him as to who He extends mercy.
"17 For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” 18 So then he has mercy on whomever he wills, and he hardens whomever he wills."
And, contrastingly, Paul shows that God may raise up those for the purpose of hardening, as well, as analogized in Pharaoh.
And we now have a clearer picture. New Covenant Jews receive mercy. Old Covenant Jews are hardened.
"19 You will say to me then, “Why does he still find fault? For who can resist his will?”
This question, then, is hypothetically from the Jew who is in the Old Covenant, who has been hardened. And Paul gives a clear answer:
"20 But who are you, O man, to answer back to God? Will what is molded say to its molder, “Why have you made me like this?”
The analogy of the potter and the clay pretty clearly comes from Jeremiah, where the clay is, just as it is here, the nation of Israel, and the potter is God. And the analogy works well, as God is justified in doing as He wishes with His nation.
Except that now, rather than one kind of pot, there are two kinds:
"21 Has the potter no right over the clay, to make out of the same lump one vessel for honorable use and another for dishonorable use? 22 What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, 23 in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory—"
And thus, the nation of Israel minus the sub group, the older, the Old Covenant find themselves prepared for wrath, and the sub-group, children of the promise, the younger, the New Covenant find themselves prepared for glory.
And the hypothetical Old Covenant Jew is disarmed, because the prophets (Jeremiah) do say that God may do as He wishes with His people, especially as they are an obstinate and disobedient people who, in the analogy of the vineyard workers, killed the son.
So, we can conclude a few things from what we see up to this point:
1) Romans 9-11 is primarily about Old Covenant Israel and whether God's word to them (in terms of the 8 items spoken of in vv4-5, especially those promises) have failed.
2) Paul establishes a sub-group in Israel, Jews who are children of the promise, who have a different destiny than those who remain in the Old Covenant.
3) God's election in this portion was about Covenants, not individuals.