>>514792714 (OP)
The justification for Israel's existence and the extreme latitudes afforded to its government and military are predicated on their victimhood in the second world war, in which the west professed for itself a moral obligation to stop Germany's crimes against freedom and human dignity as casus belli and the failure to act early and unequivocally to that end as their culpability in their foe's genocidal policy.
Thus by supporting Israel we legitimize our victory in WW2 and the whole global order that emerged from it. However this comes with a caveat. If our legitimacy, and Irael's legitimacy, comes from our moral responsibility to intervene militarily to prevent an obvious genocide, then the plight of the Palestinians in Gaza would constitute exactly such a moral responsibility.
So we're left with a dilemma. To support the Gazans would fulfill the moral obligation which underpins our global legitimacy, but would constitute opposing Israel, and opposing Israel would undermine our global legitimacy. If we support Israel, we repeat the same mistakes that led to the events of WW2 and in doing so undermine the moral basis of our legitimacy. If WW2 was not a righteous crusade against a genocidal tyranny to liberate the free people's of the world and protect the jews from unjust persecution, then it was just yet another great power conflict between two morally equivalent ideologies engaged in a zero sum game of personal benefit at the expense of the other. If our legitimacy was won only with strength of arms, then it persists only with strength of arms and we accept that armed conflicts to challenge our world dominance is inevitable and justifiable. Nobody wants to accept that reality, because while war might be good for a state it is always bad for its citizens.