LUHE said " Israel has existed since 1948 - it also existed thousands of years ago, too."
That is not an argument for anything - it's may not be an argument but it is a pretty good point that puts this whole issue into perspective.
Jews were living in the Levant many centuries before Arabs settled the region.
The first Arabs to settle the Levant came from what is now Yemen - they were Christians from the Al Azd tribe, if my memory serves correctly. They started settling in the Levant from the end of the first century CE onwards. Muslim Arabs seeped into traditionally Jewish land from the 7th century onwards.
Jews had already been living in the same area many centuries before (Kingdom of Israel, Kingdom of Judah). So Jews do have a legitimate claim on that part of the Levant. Meanwhile, there has never been an independent Palestine.
I have a few questions for you ...
1. Palestine for the Palestinians?
2. Ireland for the Irish?
3. England for the English?