Why don't Arabs want Israel to exist?

History's legacy created divisive issues between Palestinians and Israelis. Judea, home of the Jews in ancient times, was conquered by the Romans and renamed Palestine. Palestine was later conquered and inhabited by Arabs for over a thousand years. The Zionist movement arose to restore the Jews to Israel, largely ignoring the existing Arab population. Following the Balfour Declaration in 1917, Palestine was granted to Britain as a League of Nations mandate to build a national home for the Jewish people. The Arabs resented the Jews coming in to take their land. Led by Grand Mufti Hajj Amin El Husseini, they rioted repeatedly and later revolted, creating a history of enmity between Jews and Arabs in Palestine. Britain stopped Jewish immigration to Palestine. Following the Holocaust, in which 6 million Jews were killed by the Nazis, pressure on Britain increased to allow Jewish immigration to Palestine. In 1947, the UN partitioned the land into Arab and Jewish states. The Arabs did not accept the partition and war broke out. The Jews won a decisive victory, expanded their state and created several hundred thousand Palestinian refugees. The Arab states refused to recognize Israel or make peace with it. Wars broke out in 1956, 1967, 1973 and 1982, and there were many terror raids and Israeli reprisals. Each side believes different versions of the same history. Each side views the conflict as wholly the fault of the other and expects an apology.

Originally formed to regain all of Palestine for the Palestinian Arabs, the Palestine Liberation Organization signaled that it would accept a two state solution in 1988. The Oslo accords were supposed to have led to a peaceful resolution of the conflict, but continued Israeli settlement and Palestinian violence and incitement degenerated into open conflict in September 2000.
Source:
http://www.mideastweb.org/nutshell.htm