The title of this post is drawn from a sermon I read of John Piper on Romans 9. The title sums up Paul's problem appropriately. Much of the material here is dependent upon Piper's sermon on Romans 9 (which is also fleshed out a great deal in his book "A Justification of God")
1I 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,  my kinsmen according to the flesh. 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.The problem that Paul is dealing with as he opens up chapter 9 of the book of Romans is simply that his kinsmen are accursed (anathema) - separated from God and foreigners to the Gospel.
Paul is filled with "great sorrow and unceasing anguish." He wishes that he himself could be accursed and cut off from Christ for the sake of his brothers. But this is a wish that cannot be fulfilled as he just finished Romans 8 with a proclamation that nothing can separate him from the love of Christ (Romans 8:35-39). Neither height, nor depth... not even Paul can separate himself from the love of Christ.
In fact, the problem follows directly from that passage. The Israelites have (v. 4-5) "the adoption, the glory, the covenants, the giving of the law, the worship, and the promises... the patriarchs, and from their race, according to the flesh, is the Christ." They were God's chosen people! The promises, the adoption, the glory, the covenants... all those things were promised by God for Israel, but now it seems that they are cut off from the grace of God. Indeed, the "name of God is blasphemed among the gentiles because of [the Jews]" (Romans 2:24). Israel has stumbled over the stumbling block.
So Paul turns from the praise and worship in delighting in the security of Christ Jesus to the difficult question of "what happened to Israel? Why aren't they secure in Christ? If they had the adoption, the promises, the covenants, what separated them from the love of God?"
These questions lead us, the hearers, to wonder, "has the word of God failed? Doesn't God keep his promises?" (see Romans 9:6) and lead Paul to an extended defense of God and His sovereignty in election.