What does the right to exist really mean?
What does a "right to exist" mean exactly? There is no "right to exist" for states under international law. The formula has arisen in international diplomacy uniquely regarding Israel. It does not mean simply diplomatic recognition, which is the "fact" of existence. It does not mean recognizing Israel's "right to self-determination," either, or we would be using that famous term.
Absent clear borders, recognizing Israel's "right to exist" must mean something else. And of course it does. Clearly implicit in the term is Israel's right to exist as a Jewish state. In other words, the "right" Hamas is being required to endorse is that Israel can legitimately compose itself as a state in Palestine that is populated and run primarily by Jews, primarily for Jews. Such a state would thus be authorized by Hamas to sustain whatever laws and policies necessary to preserving its Jewish majority, even rejecting the return of Palestinian refugees mandated by international law. Or building a massive Wall on Palestinian land designed to protect the Jewish state from the "demographic threat" of mass non-Jewish citizenship-i.e., the Palestinians.