[T[hose who asked the question did not understand that for Israel the only unprecedented feature of the trial was that, for the first time (since the year 70, when Jerusalem was destroyed by the Romans), Jews were able to sit in judgment on crimes committed against their own people, that, for the first time, they did not need to appeal to others for protection and justice, or fall back upon the compromised phraseology of the rights of man--rights which, as no one knew better than they, were claimed only by people who were too weak to defend their "rights of Englishmen" and to enforce their own law. (The very fact that Israel had her own law under which such a trial could be held had been called, long before the Eichmann trial, an expression of "a revolutionary transformation that has taken place in the political position of the Jewish people" ...) It was against the background of these very vivid experiences and aspirations that Ben-Gurion said: "Israel does not need the protection of an International Court."Hannah Arendt, Eichmann in Jerusalem (New York: Penguin 2006) (1963), 271-72.
It is worth noting that Arendt was quite the skeptic of trying Eichmann in Jerusalem. But nonetheless, here I think she aptly summarizes one of the key drivers as to why so many thought it was so essential that he be tried by Jews, in Jewish court, in a Jewish state.