It was with mixed feelings that we watched President Barack Obama deliver his extraordinary speech to the Muslim and Arab worlds in Cairo yesterday. Critics will see the speech as incredibly naive. Yet it was also the most meaningful and coherent attempt by an American leader since 9/11 to dissociate the world's 1.5 billion Muslims from demagogic elites preaching worldwide jihad and hatred of non-believers. It is not insignificant that Ayman al-Zawahiri and Osama bin Laden took the president's power to persuade seriously enough to try to preempt him by issuing fresh rants. It must have galled them to see hard-line imams and Muslim Brothers listening attentively in the audience. A Gallup Poll, taken before the speech, showed 25 percent of Egyptians approving of the US under Obama, compared to 6% under George W. Bush. IN A city where Holocaust denial is part of the popular culture, it was good to hear Obama telling Muslims: "Six million Jews were killed," and saying otherwise is "ignorant, and hateful." To no applause, he proclaimed: America's ties with Israel are "unbreakable." However, elsewhere, Obama's moral equivalency was disconcerting. Undeniably, Palestinians have endured dislocation - but it would have been courageous of the president to say that much of this pain has been self-inflicted, thanks to 60 years of intransigence. He was right to remind the Arab states that their peace initiative was only "an important beginning." And we were gratified when he insisted Hamas end its violence, recognize past agreements, and accept Israel's right to exist. But we cringed when he associated the Palestinian struggle with the US civil rights movement and with the campaign for majority rule in South Africa - even if the punch-line of this false analogy was: Terrorism is always unjustifiable. We were braced for his reiteration of long-standing US policy against the settlement enterprise. But he missed a crucial opportunity to prepare the Arabs for territorial compromise. No Israeli government is going to pull back to the hard-to-defend 1949 Armistice Lines. Obama didn't really need to tell Israelis to acknowledge "Palestine's" right to exist since every government since Yitzhak Rabin's has been explicit that the Jewish state does not want to rule over another people. The real question is whether a violently fragmented Palestinian polity is capable of making the necessary compromises required to close a deal. BUT THIS speech was not largely about the Arab-Israel conflict. It was an effort to pursue public diplomacy and suasion - trying to decouple the susceptible Muslim masses from the demagogic extremists who now hold such sway. That is why the president was wise to travel first to Saudi Arabia, "where Islam began," and, just before his speech, to be seen deferentially touring a mosque in Cairo - the city from where the theology of worldwide jihad first spread its vicious tentacles. The speech was brilliantly proleptic: first acknowledging Muslim grievances, then stating the American case. To the Israeli ear, the president sounded fawning, prefacing each mention of the Koran with "holy." But it was just the right tack given the task at hand. Similarly, as the president highlighted the epochs during which Islam was a force for enlightenment, we could not help but recall that even in that "Golden Age," Jews were still treated as a dhimmi people. And yet, the president's harking back to periods of relative tolerance bolstered his call on today's Muslims to behave temperately. We also appreciated his defense of the region's Christian minority. We swallowed hard as the president intoned that "Islam is not part of the problem" of worldwide terrorism. At the same time, we reminded ourselves that his goal was to convince ordinary Muslims to make this dubious statement reality. On democracy, employing a lighter touch than his predecessor, Obama advocated for the right of all citizens everywhere to express themselves freely and to live under regimes that respect the rule of law. Iran's supreme leader Ayatollah Ali Khamenei didn't wait long to digest the Obama speech before proclaiming that America remained "deeply hated" in the region, something that wasn't going to change because of "beautiful and sweet" words. Who will be the first Muslim leader to tell the ayatollah he is wrong?