In Deuteronomy 4 Moses spelled out Israel’s mission to the nations:

Keep them and do them, for that will be your wisdom and your understanding in the sight of the peoples, who, when they hear all these statutes, will say, ‘Surely this great nation is a wise and understanding people.’ For what great nation is there that has a god so near to it as the Lord our God is to us, whenever we call upon him? And what great nation is there, that has statutes and rules so righteous as all this law that I set before you today?

According to Paul, Israel had totally failed to spread this fear of God by his law. Instead of wisdom they had spread blasphemy:

But if you call yourself a Jew and rely on the law and boast in God and know his will and approve what is excellent, because you are instructed from the law; and if you are sure that you yourself are a guide to the blind, a light to those who are in darkness, an instructor of the foolish, a teacher of children, having in the law the embodiment of knowledge and truth— you then who teach others, do you not teach yourself? While you preach against stealing, do you steal? You who say that one must not commit adultery, do you commit adultery? You who abhor idols, do you rob temples? You who boast in the law dishonor God by breaking the law. For, as it is written, “The name of God is blasphemed among the Gentiles because of you.”

What is obvious here is that Paul spends no time trying to convince Jews that they have indeed broken the Law. Quite the contrary, he writes as one who is sure that they know and admit to the truth of the situation.

What is also obvious is that Paul does not write to people who are trying to keep the Law but are failing to measure up despite all their efforts. He is speaking to people about their nation and its reputation for willfully violating the Law.

So in what way does Paul’s Jew “boast in God”? If Paul had felt compelled to make a case against the Jews that they violate the Law we might suppose that they boasted in keeping the Law. But that is not the case. They boast in having been entrusted with the Law. They boast that they possess the Law and therefore possess, they think, God.

Paul’s message is like John the Baptist’s:

And do not begin to say to yourselves, ‘We have Abraham as our father.’ For I tell you, God is able from these stones to raise up children for Abraham.

So the Jew’s boast that they are Jews who have the Law by nature–i.e. by birth. But Paul says that this possession of the Law will not justify them. They are supposed to actually keep the Law.

For circumcision indeed is of value if you obey the law, but if you break the law, your circumcision becomes uncircumcision.

For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin.