Asking Palestinians to say that Israel has a right to exist is like asking Native Americans to say the USA has a right to exist. What about Israel exists and has the right to continue to exist?
The good old "we were first, so we're the only ones who belong here", which always brings up the question, how far we want to go back in time to determine who really was first. There is no answer to this question, hence it's the reason for so many conflicts across the globe and through history.
Eh, I don't think many societies besides America are as open as America to migration and immigrants (and we have strong anti immigrant streaks sometimes, but I think we're more tolerant than most). Like Japan is an old society that's just not used migration/immigration. Hell, the shogunate shut out people coming in or leaving for 200 or so years before 1850. And even old Western societies that have a colonial past and immigrants resulting from that are not as open to immigrants as the US (I mean that's what Brexit's about, right? And you saw how destabilizing Syrian and Libyan refugees have been to the EU, and how incompletely integrated Algerian immigrants are in France).
But Jews were expelled a long time ago from their home, and only started coming back with the Zionist movement. But with respect to the creation of modern Israel, obviously the Palestinians were there before the Zionist movement and the creation of modern Israel, and I think they might feel the same way about the creation of Israel as maybe Native Americans might feel about European colonization and the creation of the US.