Toynbee was casually anti-Semitic (he considered Judaism to be a "fossil"), a sentiment that was hardly uncommon amongst elite Englishmen of the time period. And his main charge -- which prompted the debate challenge in the first place -- was his claim that Israel was morally equivalent to Nazis. Then, as now, this claim was trotted out without any sense of proportion: "Nazi" was little more than a stand-in for "person who did bad things"; because Israel had undoubtedly done bad things in the War of Independence, Israel was akin to a Nazi state. The problem, as Herzog observed, is two-fold.
First, "Nazi" is not in fact accurately used to describe an otherwise run-of-the-mill state that committed some wrongdoings. To diminish Nazism to such genericism is in effect a form of Holocaust denial -- it replaces the incredible magnitude and gravity of the Nazi Holocaust with a vague wave at condemnation. One sees this too with how some people treat racism -- stripping away the sheer sweep of centuries of ruthless murder, rape, terrorism, and enslavement; replacing it with some bromide about how for awhile we may not have quite lived up to our highest moral ideals. And if that's all racism ever was, then sure, every time President Obama suggests a policy proposal we find objectionable really is "just like slavery."
Second, if "Nazi" really does mean nothing more than "state which has committed a wrongdoing," then not just Israel is guilty. The UK is a Nazi state. America is a Nazi state. India is a Nazi state. Each of Israel's Arab adversaries is a Nazi state. Palestine will be a Nazi state. So why, then, should Israel be uniquely called out for being a Nazi state? If "Nazism" really is that mundane, it's almost not an observation worth making. But what's really happening is that Jews are being asked to meet an idealized standard of justice expected of nobody else, and when they inevitably fail to do so it is not seen as failing "normally", but rather as sharing space with the most monstrous of monsters.
But all of this, to me, raises another questions, which is "why Nazi?" If what we're really talking about is just a banal form of evil -- or hell, even if we're talking about much more serious, extreme evil -- Nazis are hardly the only choice we have. As offensive as the "apartheid" state analogy is, I will credit it as being less offensive than calling Israel and Jews Nazis. The reason people use Nazi this way -- divorced from the actual historical significance of the term, untethered from any proportionate sense of what the Nazis actually did -- is that it wounds Jews. That label appeals over all other ones because it has the unique capacity to hurt Jews on account of their Jewishness. It's akin to "criticizing" a Black person by calling him a plantation owner, or a lynch mob leader. It gains its power from a history of oppression, and when you are leverage historical oppression against the oppressed, that's prima facie evidence of racism or anti-Semitism no matter what your motives are.
Within all this, it is important to remember what the Holocaust actually "establishes" as relevant to contemporary discussions about Israel and Jews. Many people contend that Jews think the Holocaust has rendered them "perfect", unassailable, or immune from criticism. They seek to leverage the rhetoric of the Holocaust against Jews so as to remove this allegedly illicit gain, this wrongful bounty we illegitimately seized after being so lucky as to have been subjected to mass murder. But the Holocaust does not establish Jews are perfect -- it establishes that non-Jews aren't.
The fact of the Holocaust and other acts of anti-Semitism doesn't establish that Jews are unassailably virtuous. Why would it? There's nothing about oppression that purifies its victims -- imperfect people can be victims too. What it establishes is that non-Jews are not perfect; it destabilizes the hegemonic presence of non-Jewish voices and thus creates space for Jewish voices to be heard. To the casual observer that looks like a claim that Jews are "perfect", but that's only because Jews are claiming the right to speak on equal terms with a non-Jewish presence that had previously arrogated to itself a label of universal transcendence.(Original Tablet link via Daniel Goldberg)
The frame that oppression makes the oppressed "perfect" is really more of a reactionary step. The framework sets up for Jews (and other minorities) a standard they can't possibly meet. And once they fail to meet it, it justifies stripping the label of "victim" and returning to the status quo where they can safely be ignored. It obviates the need to problematize the non-Jew in favor of providing a temporary elevation of the Jew to non-Jew status, contingent on the Jew maintaining a standard of conduct that nobody else can or is expected to meet.