The borders for both Palestine and Israel were drawn up by the Europeans and Americans (PROTIP: not the Jews nor the Muslims). Neither side willingly stole each other's land, but were put into this position by people who believed that they could profit from the conflict, facilitated by the strategically drawn borders.
For the Palestinians: They were on the land at the time the borders for Israel were drawn, and were forced to move. In most cases, defending your territory from occupiers is justifiable. Going up against a nation with a well-trained army, backed up with American firepower/funding makes it that much harder.
For the Israelis: They were put there, in the middle of a bunch of nations/cultures that hated them. They were not an invading force by choice. They were pretty much forced to settle there by others, and whether they were right or wrong, they now have to fight practically every day of their lives to survive in certain areas.
Neither side of this conflict wins. Both sides have their share of fundamentalists as well. The Palestinians have Hamas, and others, who condone suicide bombing and the killing of innocent civilians. While Israel operates on a much different seemingly more acceptable set of rules of engagement, the magnitude of their retaliatory strikes and their refusal to differentiate between fighter and civilian goes to show that they're just as eager to kill as their opponents.