It is an unfortunate fact that some issues are so intractable that they are virtually impossible to solve unless one side abandons a key component of its raison d'etre.
The Arab Israeli conflict is such a problem, but it is not just the Arab wish to terminate Israel, but that is the sticking point that we most often hear about. There is a fundamental fact -- the elephant in the room that no one wants to mention -- that Israel is one of the few states that is based on, as the essence of its existence, one race/religion. As such it is more like Iran than the U.S.A., though a great PR effort by Israel sells it as a "Democracy", pure and simple. Like it or not, Israel is not ABOUT being a democracy. It is ABOUT being a Jewish state. We can all sympathize as to why this happened after the horrors of World War Two.
Nevertheless, no matter which way you cut it Israel is a state based on exclusion and not inclusion. That makes it the virtual opposite of the United States, which at least philosophically is all about inclusion.
The Arab point, though obscured by stupid counter productive actions on a consistent basis that shoot themselves in the foot more than they affect Israel, has to be that the existence of Israel is not just about taking land from the Palestinians who where there, and giving it to foreigners who came from Europe, Russia, the Americas and elsewhere, but to be about the fact that because the state was based on race/religion it was a double affront as Arabs were by definition excluded. Yes, there are token Palestinians in the Israeli Knesset but this is cosmetic at best and there is no question that an Arab would ever really participate in Israeli society as an equal. The Israelis freely admit this and many object to this fact.
For most people in the world, the idea that God is a real estate agent who would give a particular piece of land to one particular racial group, or that there is a "chosen people" at all, are preposterous ideas from the start. Especially since reference to these supposed God directives were indicated in a book written by people who thought the world was flat and the Sun and planets revolved around the Earth. Therefore it is hard to justify an inherent "Right" for Israel to exist because to accept that, one has to accept all sorts of bad things we read about in the Old Testament, like genocide and lots of other stuff that 99.9% of humanity would laugh at if put to the test.
Meanwhile, it is also relevant that since its creation many Israelis were born there through no fault of their own (perhaps even a majority by now) and therefore by birth have nowhere else to go. They are a fact as much as the Palestinians who were thrown into refugee camps are a fact. They cannot go back where they came from. They are of that land now too.
So what is the solution? There can only be one, and that is the one state solution where the Israelis actually accept the concept of democracy as the prime directive as opposed to race/religion as the prime directive PLUS the idea of a multi-ethnic/religious state where all within its boarders are equal under the law. The Palestinians would have to accept the same idea which is actually less of a stretch than the one the Jewish Israelis would have to deal with. Once the idea of the Jewish-only state ends the possibility of a multi-ethnic union becomes possible. Without that there is no hope.
This sort of solution is never easy at first but lets remember that Canada, Belgium, Switzerland, India, England and many other countries are made up of several groups even with different languages but still manage to have a union that works. Europe is all about joining different national groups together for mutual benefit. Israel could be the catalyst for this in the Middle East but by calling itself the "Jewish State", it will always be setting itself apart and exclusionist. The same is true for Iran calling itself an Islamic state. Such pronouncements are inherently limiting to a nation and society. Excluding participation to a group within a society whether it be women, people of a different color, race, religion will always put that society at a disadvantage. Restricting new recruits to a society to one ethnic/religious group is just as limiting. Israel is a nation that has certainly experienced this disadvantage and suffers for it on a daily basis. If the US did not provide such a hefty foreign aid package to Israel and Jewish donations from around the world dried up, Israel would also dry up. That has to be a dangerous dependence. What is most stunning is that some of the greatest forces in liberal and high minded moral thinking are Jewish. Want support for a charity, even ones that help Palestinians, the Jewish community will almost always be in the front of the line. Israel therefore represents a strange moral dichotomy.
The United States has benefited by a policy of welcoming everyone and incorporating them into the society. When in our past we excluded sections of the population, we suffered for this and lost the potential contributions those groups could have made. It is not perfect and we have hiccups but the principle exists. Europe is trying the road of inclusion and bringing disparate nationalities together for mutual benefit. That is the road of the future. It will inevitably have to be the road for the Israelis if there is ever to be peace in that region. Exclusion and exclusivity is never going to be a winner in the end.