The people actually lived in peace long before last century. The trouble started in 1948 when the UN granted the Jews a homeland. The Arabs went to war so as to push the Jews into the Med. Got much worse in the Six day war when they were humiliated by a numerically inferior people fighting for their homeland and their very lives. When the Palestinian speaks of a two state solution and peace in English, in Arabic they are saying nothing of the kind. They want nothing less than to kill every last Jew. Just like their prophet taught them to.
The Jews, under world pressure and hoping to appease their retractors pulled out of Gaza, hoping it would bring them peace. Instead it brought them a hostile state from which hamas could continue attacking Israel non stop. If they were to pull out of the Left Bank as well, they would be committing suicide.
Did you make that up or are you repeating what you've been told? There was peace under Ottoman rule, but when the Ottoman Empire crumbled, various factions (egged on by various European powers) started to fight over what form the new government(s) would take.
Most historians generally agree the fighting between Arab and Zionist nationalists got underway in 1920. There was a battle and a riot that year, another one in 1929, and another one in 1933, and every one of them was the result of rising tensions as European Jews began to systematically settle the area with the goal of establishing a Jewish State. Things got worse in the mid- 1930s, which is when Zionist terrorist organizations like the Irgun, Lehi, and the paramilitary Haganah became very active. The conflict intensified shortly after WWII when Zionist terrorism was in full swing, and survivors of the Holocaust were flocking to the region, determined to create a Jewish State for where Jews would never be a minority. And then the UN came up with a partition plan that was grossly unfair to the Palestinians, the Zionists implemented Plan Dalet to seize the best agricultural land, industrial areas, and resources, and guess what? The fighting got worse.
Also, Israel did not withdraw from Gaza to appease anyone. The containment walls were finished, Egypt had been bribed by the US into keeping their mutual border with Gaza closed, and it was too risky for the IDF to try to protect idiot religious fanatics who wanted to be locked in with millions of destitute, displaced Palestinians. So the idiot settlers were removed by force, and the isolation of the Gazans was complete.
There was never any chance imprisoning the people of Gaza would bring about peace, but Israel expected to be able to beat and starve them into submission, which some people apparently think is the same thing.