Both are mistaken. Palestinians have shown they won't swallow an endless, humiliating occupation, and Israelis have proven they have the will and the power to preserve their homeland whatever the cost.
Yet each side persists in what it should know to be utter folly. The Palestinians keep dispatching suicide bombers in the hope of breaking Israel's resolve, but the effect is merely to alienate even the most dovish Israelis. The Israelis roll tanks into Arab villages to prove the futility of terrorism, a strategy that only spawns more volunteers for bloody martyrdom.
The maddening aspect of the conflict is not that there is no solution, but that the solution is so obvious and yet so unattainable. Both sides want all or much of the same land. So there is only one thing to do: divide it in a way that will satisfy neither.
But that's the one thing they aren't prepared to do.
The Israelis and Palestinians are like two starving men with one meal between them. If they share it more or less evenly, each will still be hungry. Understandably, each prefers to have it all. But the consequence is that they spend all their time fighting, while the food spoils.
The decision by Sharon to launch an all-out war against the enemy has a certain visceral appeal, particularly when viewed against photos of Jews slaughtered at a Passover dinner. But in this context, military force is a temporary remedy, if that. Israel can destroy military targets, but the military targets are not where the real threat lies. It lies in the mass of the Palestinian people.
"No matter how many tanks go through how many villages," said Secretary of State Colin Powell last week, "at the end of the process you will still have suicide bombers."
Sharon has isolated Arafat, and says he would be happy to give him "a one-way ticket" out of the country. His army may end up killing him, accidentally or on purpose. But while it would have been useful to the Allied cause to assassinate or incapacitate Hitler, this is a different sort of war. Arafat is less a leader than a follower of his people, and removing him would no more stop the violence than lassoing one steer would stop a stampede.
The main source of friction between Israelis and Palestinians is the Israeli occupation. Sharon's military assault might make sense as a prelude to a withdrawal from nearly all of the West Bank. But it appears to be more a prelude to continued occupation, and the Palestinians have already made clear their response to that.
The Palestinians, of course, might have rid themselves of the occupier had they been more willing to compromise in the Camp David negotiations two years ago. But they weren't ready to surrender the right of Arab refugees to return to their homes in Israel, just as the Israelis weren't ready to give up many of their settlements or to consider dividing Jerusalem. So Arafat walked away, and a new intifadah erupted.
And what has it accomplished? About 1,200 Palestinians have died in the violence, and Israeli public opinion has hardened against even the terms offered by Prime Minister Ehud Barak at Camp David - not to mention that there are Israeli tanks and troops making war in Ramallah, Bethlehem and other Palestinian cities. That can't be a great comfort to Israelis, who are paying a terrible price themselves for spurning the concessions that might have yielded a historic breakthrough.
The current violence came about only because neither side was willing to take some very painful steps - with the result that both are enduring a different kind of agony. The Israelis and the Palestinians have a hundred ways into war, but none that lead to peace.
Steven Chapman is a columnist for the Chicago Tribune.