The most likely incorrect (or at least, incomplete) understanding I have of the "Isreal problem" goes a bit like this:
At some point, the jews leave the physical locality of isreal. (This has happened before in history after judea was captured by the persians)
The jews still view the physical locality of isreal as their ancestral homeland.
Other people move in after they are displaced, and make it their home. (Nature abhors a vacuum)
This dispersed diaspora of jewish people gets blamed for a lot of shit, some true, some false. (Comparison, The Roma people, aka gypsies)
This persecution results in the Nazi genocides against them, as well as a cultural identify of being persecuted/wronged.
As a gesture of good will toward them, the allies do what they shouldnt have done, and gave the territories that the nazi's captured in the second world war that were of significance to the jewish people, TO the jewish people. The nazis had captured the jerusalem area with minitary force from the other indigenous peoples.
This pisses the indigenous peoples off, and starts the "Destroy isreal!" motive. The people that were kicked out by the nazis wanted to go home, but couldnt, because the jews were there now, and the allies were protecting them.
A coalition against this occupation reached a head in the 60s & 70s, when Egypt invaded, and was subsequently defeated, which is when isreal annexed the west bank.
This annexation, coupled with the zionist nationalist phenomenon, displaced even more indigenous people, making things worse.
The indigenous people want the jews gone. The jews view their claim to the land as being literally god-given, and sacrosanct.
There is no solution to this problem.