Anyone who hears with the ears of a 1st Century Jew, regardless of what that person thought of Paul, would ask the question that opens up Romans 3: “What advantage, then, is there in being a Jew, or what value is there in circumcision?” Again, Paul surprises.
Paul responds in two ways: first, he says the Jews have been entrusted with the words of God. (The NIV’s and TNIV’s “very” before “words of God” is not present in the text.) It’s good enough to have the words of God, the logia of God. The Jews were given these “oracles” so they would live them and share them with the world so they could become a blessing to the world.

Point of observation: Paul here connects God’s “faithfulness” (3:3: pistis theou) with God’s righteousness (3:5), rendering the idea that God’s righteousness is at least expressed in his covenant faithfulness to his promises to Abraham — which was what? That they would be a blessing to the nations. (This, by the way, is a huge debate for the New Perspective people and its critics.)
Second, he shifts some to another concern: the unfaithfulness of Jews to fulfill their task of obeying Torah in order to be a light to the nations, however, does not render God unfaithful to his promises. God is true, humans are the ones to blame (Rom 3:3-4).
And then Paul, true to his idea chasing pattern, explores yet another idea: Israel’s unfaithfulness actually leads to God’s righteousness. How so? In two ways, by showing off his grace in restoring both Jews and Gentiles by faith in Christ and, secondly, by rendering judgment on the unrighteous, unfaithful Jew. Which leads to his comment: God’s glory issuing from such a process does not let the unfaithful Jew off the hook (3:5-8). It is really a silly, pedantic piece of logic that some might use: “If my sin leads to God’s display of his honor-bringing grace, then I should be complimented for my sin!” (And Paul makes it doubly clear by using the first person; he stands in for those who would use such logic of themselves; he stands in for the Jew who makes such claims.)
Paul’s point though needs to be seen for what it is: Israel’s unfaithfulness does not stop God from bringing about his redemptive plans for his created world.