People ask this question as if Israel is a unique State in the world, as if the answer to this question is some kind of divining rod indicating one's position on Middle Eastern politics, or the Jewish people. In reality these things are irrelevant to the question. Does Israel have the right to exist? Of course not. It's an absurd thing to claim. No State has the right to exist. People have the right to exist, and people have a right to establish societal institutions. They even have a right to name such an institution "Israel" if they wish. What they don't have the right to do is impose their societal institutions on other people who do not consent, because those institutions have no rights independent of the people who comprise them. Free people always retain the right to alter or abolish the societal institutions they have created or inherited, so no such institution can be said to have an independent right to exist.