Hebrews 8:8-9 (ESV)
For he finds fault with them when he says:
"Behold, the days are coming, declares the Lord,
when I will establish a new covenant with the house of Israel
and with the house of Judah,
 not like the covenant that I made with their fathers
on the day when I took them by the hand to bring them out of the land of Egypt.
For they did not continue in my covenant,
and so I showed no concern for them, declares the Lord.
God lays down the reason that he is establishing a new “covenant”. Why does he do this? Because the people haven’t followed, they did not continue in the old covenant. He says that because of this he has shown no concern for them. They didn’t live up to their end of the bargain is one way of putting it, God brought them out of Egypt, but they decided the other gods were more fun to worship. They did not follow God’s law. God considered it a bad covenant.
He loved Judah. He loved Israel. He covenanted with them, because he loved them. But then they angered him because they failed in the covenant. It is like making a business deal with a friend, nothing can sour a friendship faster! It angered God.
The Israelite often receive a hard time for this. People read the Old Testament and can’t believe what they are seeing and reading. Well think of it as a mirror. You would not have done any better. This is also the fallacy of modern evangelicalism, and millennialism, that often sees the Old Testament as being valid for Jews even today, as if God saves them by it. Get a grip, even their Old Testament points to the inadequacy of this covenant, and the need for a new one. Shame on anyone who knows of Christ, his death on the cross, and then tells a Jew it is o.k. for them to continue with the old covenant!
The New Testament is now in play, and it is the only way anyone can be saved, Greek or Jew. The Death of Christ, is our salvation.