Yeah, but since the place was called Palestine, everyone there was Palestinian. This includes Jews. During the British Mandate, Arabs revolted against the British and Jewish terrorist groups did likewise, and increasingly the Arabs and Jews fought each other as well. The UN tried to broker the two state partition - one for Jews, one for Arabs. That fell apart, primarily due to the Arabs rejecting it. But the UK wanted out of the whole mess, and they weren't going to wait for a real solution, so they basically left, with nobody 'officially' in charge. Chaos naturally ensued. The Jewish state took over and Jewish partisans removed Arabs from many villages in what would have been the Arab partition. Arab countries nearby responded by attacking (as most of them had already indicated they would do, after the Palestinian Arabs rejected the partition deal).
And it has been tit for tat ever since.
More background:
Mandatory Palestine - Wikipedia