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Short answer
The Palestinians could have already had their own state in 1948! But they chose to reject the UN partition plan and go to war instead with the Jews.
Long answer
Palestinians had multiple opportunities to form their own state, most notably the 1948 partition plan by the UN, and in 2000 when the Israeli government, alongside former President Bill Clinton offered a Palestinian state. However, these offers of a two-state solution were repeatedly rejected by the Palestinians. Challenges to the peace process such as the rise of Hamas have complicated matters, and the Arab rejectionism has led to further conflicts and missed opportunities.