> We can acknowledge that some Arabs were forced out of some towns during the war
That's a massive understatement. The Zionists / Israelis[0] expelled 80% of the native population of the territory that became Israel in 1948.
Across Palestine, Zionist / Israeli forces carried out a campaign of ethnic cleansing, with the goal of capturing as large a territory as possible with as few Arabs as possible.
In Haifa, Zionist forces first carried out a campaign of terrorism, which caused nearly half of the Arab population to flee. Then, they launched a massive attack on the Arab neighborhoods, deliberately shelling civilian areas and using psychological warfare (threatening radio broadcasts in Arabic, for example) to try to convince the local population to flee. By the end, more than 90% of the Arab population had fled, and the city fell to Zionists forces.
This pattern was repeated across Palestine. The area that eventually became Israel had a large Arab majority: 60% to 40%. After the Israelis were done kicking out the Arab population, less than 15% of the population was Arab.
> the Arab armies forced out every single Jew from the areas they conquered during the same war.
The Arabs hardly conquered any territory in 1948. They were largely on the back foot. The vast majority of people who were violently expelled from their homes in 1948 were Arab.
> However, the core of the conflict is the Arab side insisting that Jews have no right to any land between the river and the sea simply because of who they are.
That's what you think the "core of the conflict is"? Not the fact that a foreign people came into Palestine and announced that they were going to turn it into their own country - and then actually did so through the expulsion of 80% of the native population? The goals of the Zionists made war with the native population completely unavoidable. Do you think that any population anywhere else on Earth would have allowed their country to be taken over by a foreign people - who wanted to establish their own state on it - without resisting?
> You think that Jews of European heritage have some fundamental un-right to live in Petah Tikva?
You talk about this as if it were just a few people immigrating to a foreign country and wanting to settle down among the locals. That's not what Zionism was. It was a movement that aimed to turn an Arab land, inhabited almost entirely by non-Jews, into a Jewish state, regardless of what the native population wanted. It was essentially a foreign invasion, facilitated by the British Empire, which held down the locals long enough for the Zionists to gain a strong foothold in Palestine.
> Many Europeans and Americans oppose the immigration policies of their governments. Can they claim in 100 years time that the migrations were illegal?
You keep talking about Zionism as if it were just a few immigrants arriving in a country and settling down. Are Mexican immigrants in the United States part of a large, organized movement that has declared that it will turn the United States into a new Mexican country for Mexicans alone? Zionism was an attempt to turn Palestine into a Jewish state. The locals were not even consulted. They were forced to accept it by a foreign empire - the British Empire - that ruled over them undemocratically.
0. I use this term because Israel was officially founded in the middle of the conflict. Zionist paramilitaries became the Israeli army.