Both believe that the land belongs to them.
Historical background: The land was called Philistia when the Romans had control of the land. Palestinians are Arab speaking people who were from other Arab countries, however, they weren't for some reason allowed to go back to their homeland . It is said that Palestinians never really had control of Philistia. The land was actually under the rule of the Ottoman Empire (lasted about 400 years I believe), the British (from 1918, I believe to when the UN declared Israel a nation in 1948), and Israel.
I personally don't agree with the ideology that both sides are right because historical artifacts that have been found, lead to me believing that Jewish civilization has been in the region a lot longer than Palestinians. There have been a lot of artifacts under the Temple Mount, where the Dome of the Rock sits, that lead archeologist's to believe that for at least 3,000 years there have been a remnant of Jews who have lived in Israel.
Hopefully this helped and good luck.
