"Recognizing Israel's right to exist," the actual demand being made of Hamas and Palestinians, is in an entirely different league. This formulation does not address diplomatic formalities or a simple acceptance of present realities. It calls for a moral judgment.
There is an enormous difference between "recognizing Israel's existence" and "recognizing Israel's right to exist." From a Palestinian perspective, the difference is in the same league as the difference between asking a Jew to acknowledge that the Holocaust happened and asking him to concede that the Holocaust was morally justified. For Palestinians to acknowledge the occurrence of the Nakba – the expulsion of the great majority of Palestinians from their homeland between 1947 and 1949 – is one thing. For them to publicly concede that it was "right" for the Nakba to have happened would be something else entirely. For the Jewish and Palestinian peoples, the Holocaust and the Nakba, respectively, represent catastrophes and injustices on an unimaginable scale that can neither be forgotten nor forgiven.
To demand that Palestinians recognize "Israel's right to exist" is to demand that a people who have been treated as subhumans unworthy of basic human rights publicly proclaim that they are subhumans. It would imply Palestinians' acceptance that they deserve what has been done and continues to be done to them. Even 19th-century US governments did not require the surviving native Americans to publicly proclaim the "rightness" of their ethnic cleansing by European colonists as a condition precedent to even discussing what sort of land reservation they might receive. Nor did native Americans have to live under economic blockade and threat of starvation until they shed whatever pride they had left and conceded the point.