Although there are a number of different reasons that you could blame for this conflict, I would say that the Israeli-Palestinian conflict started because of European Jews’ desire to escape from the anti-Semitism that was so prevalent in Europe. This desire led to the Zionist movement which, in turn, put large numbers of Jews in Palestine where they came in conflict with the people who already lived there.
In 1897, a man named Theodor Herzl convened the First Zionist Congress. The Congress’s purpose was to promote the idea of a state for Jews where they could be free from the anti-Semitism of Europe. Anti-Semitism had existed in Europe for centuries and had flared up recently in the form of a large number of pogroms in the Russian Empire in the time period 1881-1884. Jews like Herzl felt that they needed their own country so they would not have to live among people who hated them.
This idea gained momentum after WWI when the British were given a mandate over Palestine by the League of Nations. The British had promised the Arabs that the countries of the Levant that had belonged to the Ottoman Empire would be independent after the war. However, they had also promised the Jews a national homeland in Palestine. Because of this promise (the Balfour Declaration), hundreds of thousands of Jews emigrated to Palestine. In 1929, the first major incidents of violence broke out between the Arab natives of Palestine and the Jewish immigrants.
After WWII, the problem got worse. Horrified by the Holocaust, the West decided to give Jews their national homeland. This happened with the creation of the state of Israel in 1948. At that point, the people that we now call Palestinians either left their homes in what is now Israel or were forced out. Their anger at the creation of Israel and the loss of their homes helps to drive the conflict today.
In this way, we can say that the root cause of this conflict is the fact that the Jews of Europe wanted to escape from the anti-Semitism of Europe by creating a state of their own in their ancestral homeland of Palestine.