Israel claims that it was originally their land thousands of years ago. Palestine claims... Pretty much the same thing. I don't feel like either one could be in power without oppressing the other... What options are the public eye not seeing?

This is an absurd distortion. Palestinians actually were on that land 100 years ago. The ancestors of Israelis were overwhelmingly in Europe (and anglosphere states) at that time. Go back another century, and the answer is the same, go back 500 years and the only difference is the relative lack of colonists in Australia and the Western Hemisphere. The Israelis have the Old Testament for their claim, Palestinians have real world history.

There were a tiny number of Palestinian Jews who did live in Palestine, some of whom are a tiny number of Israel's current population, but these people were a prop used by the western Allies in the postwar period to create a settler-colony of European/Anglosphere Jewish people, who were funneled into the region.

I'm going to move in to your house, start sleeping in your bed, and fucking your wife. Because the prophecies in my holy book say I can. Neither of us is interested in coexisting. Which of us should leave?