Why is it so important to Jews that they call themselves children of Abraham?

Answer 1

Jews actually normally call themselves Children of Israel, the grandson of Abraham. The reason Jews call themselves this is because Jews believe that their ancestors are Abraham, Isaac, and Jacob (Israel). Since the Jews are decedents of these patriarchs, the Jews are their children.

Answer 2

Only some of Abraham's descendents were Jews. Abraham was told he would be the father of many nations. He was the father of Ishmael, whose descendants are some of the peoples of the Middle East. He was also the father of Isaac, who was the father of Jacob. Jacob's name was changed to Israel when he became the prophet of God's people. Jacob had 12 sons, who were the twelve tribes of Israel. One of those sons was Judah. The Jews are descendents of that son and are the tribe of Judah. At one point, ten of the tribes, who were righteous, asked God to take them away to a place where they could be safe from both their enemies and from the sin in the world. The Lord did so - He took them North, hence the Lost Ten Tribes. What remained were the tribes of Judah and a part of Benjamin. (This part of Benjamin was eventually absorbed into the tribe of Judah.) King David was from the tribe of Judah, and Jesus Christ was a descendent of David through his mother, Mary, since his father was God. (Though both Mary and Joseph were Jewish.) 600 years before Christ was born, Israel, now consisting of only Judah and Benjamin, were defeated by Babylon. Jerusalem was destroyed and many were carried away captive into babylon. All the years until the birth of Christ, the Jews were subject to other nations, and eventually subject to the Romans, as was the case when Christ was born.