Through their failure under the test of the law, Israel was to learn that they are unable to keep the law and that they have no righteousness by the law (Rom. 8:3a; 9:31; 10:3). It is impossible for any fleshly person to have righteousness by the law.
The sinful nature of the people of Israel cannot be changed, just as a Cushite cannot change his skin or the leopard its spots (Jer. 13:23).
Jeremiah 17:9a says, "The heart is deceitful above all things / And it is incurable." Since Israel's heart was deceitful and incurable and their nature was sinful, it was impossible for them to keep the law.
Through their total failure in keeping the law, Israel was also to come to know that they needed Christ to be Jehovah as their righteousness (Jer. 23:6b; 33:16b; 1 Cor. 1:30). Christ, the very God and the Savior, must be their righteousness.
Finally, through their failure in keeping the law, Israel was to know that they needed to have the divine life with its law in the new covenant of God (Jer. 31:31-34; Heb. 8:8-12; 10:16-17).