Why? Because they did not pursue it by faith, but as if it were based on works. They have stumbled over the stumbling stone,  as it is written, “Behold, I am laying in Zion a stone of stumbling, and a rock of offense; and whoever believes in him will not be put to shame.” (ESV)
Paul concludes this chapter with the reason why the Jews did not succeed in attaining righteousness. The Jews understood that God's Law was holy. They viewed it as a prescription for works. What they failed to realize is that there are not enough works in the world that could attain for them any shred of God's righteousness. They failed because they did not pursue righteousness by faith.
The Jews had Abraham as their "father." As Scripture declares, "Abraham believed God and it was credited to him as righteousness. Instead of being known as those who were people of faith, believing in God, the Jews were known by their efforts to keep the Law. The Law was only kept by one person; Jesus Christ himself, the author of the Law.
Paul speaks to this truth when he speaks of the "stone of stumbling," and "rock of offense." These are references to Jesus Christ himself. The Jews stumbled over the very one who came to fulfill the Law for them. The Law brought punishment because no one could keep the Law. Jesus took the punishment of our "law breaking" on his back at the cross.
Instead of the Jews gladly embracing the Savior they rejected him. It was the Jews who had him put to death. Peter speaks of this in his sermon on the Day of Pentecost. Throughout the years there have been a remnant of Jews who have followed Christ, but sadly there are many who continue to stumble over the rock of Jesus Christ.
The bottom line is that all of us must attain righteousness by faith, not works. Are you relying on your own efforts to be made right with God? You will fail. Believe in Jesus Christ, the Rock. Whoever believes in him will not be put to shame.