Paul had never been to Rome and he was eager to go there. Many disciples might have found the city intimidating with its pantheon of gods—which included the imperial cult that worshipped Rome and its emperors. To go to the Eternal City proclaiming that Jesus was Lord (rather than Nero) was something that could be detrimental to your health.
But he wanted to go there. He had been blessed by God and he felt a debt to share that blessing with others. Furthermore, he was convinced that the good news of Jesus was more than a match for the religions of Rome. The gospel was “the power of God” for salvation because in it “the righteousness of God” is revealed.
“The righteousness of God” is not primarily about us, as in God’s plan for making man righteous. It is primarily about God (through it includes us) and His personal righteousness. The gospel is the good news of God’s righteousness (i.e., His faithfulness in keeping His promises). After all, in the end our hope isn’t ultimately based on what we’ve done—it’s based on who God is. If He isn’t the loving, merciful God who keeps His promises, then we have no basis for hope of any kind.
All of this brings us to the issue Paul addresses in Romans 9-11. From the perspective of many Jewish people, it didn’t appear to them that God was being faithful. After all, if salvation was from the Jews (John 4:22), then how was it that so many of the Jewish people were unsaved according to Paul’s gospel? As a nation they had been in a covenant relationship with Yahweh for fifteen hundred years and now many of them were no longer in such a relationship with Him. It didn’t seem to them that Yahweh had been faithful.
The short, simple answer of course was that they had not embraced Jesus of Nazareth as the Messiah. But Paul doesn’t give the quick answer (to start with) because he’s not interested in writing them off, he’s interested in reaching out and to do that means that he needs to honor their question with an in-depth answer. That’s why he takes three chapters to explain why many Jewish people are now on the outside looking in.
He begins by re-telling their history from Abraham to the exile (9:6-29), exposing their superficial, selective understanding as it related to God’s election. He shows them that God has not forgotten anyone but has remained faithful to His redemptive purposes for everyone despite the nation’s faithlessness. The word of God has not failed but the people of God have.
This leads to the situation Israel didn’t see coming—those who were lost (the Gentiles) have been found while those who were found (Israelites) are now lost (v. 30ff). This prompts an important discussion of righteousness that you can read about here.