This has been updated to reflect news developments.

Of all that’s been said and written about the war between Israel and Hamas, nothing has cut through the mental fog quite so brightly as a remark this month from Hillary Clinton on “The View.”

“Remember,” the former secretary of state said, “there was a cease-fire on Oct. 6 that Hamas broke by their barbaric assault on peaceful civilians and their kidnapping, their killing, their beheading, their terrible, inhumane savagery.”

Those three words — “that Hamas broke” — aren’t trivial. They give the lie to the “Cease-Fire Now” mirage, or imposture, that has become a rallying cry at pro-Palestinian demonstrations. They are at the heart of what the war is about, and the key to how it can end. And they are the bright dividing line between those who would allow Hamas to get away with murder, and those who would refuse.

Why should it matter that it was Hamas that broke the cease-fire when Palestinian civilians are being killed in large numbers by Israeli bombs and bullets? Those saying that it shouldn’t matter argue that questions of culpability become secondary, if not irrelevant, when kids’ lives are at stake. If Israel has the power to save those kids by halting its campaign, goes the argument, then it has a moral obligation to do so.

But wait: Doesn’t Hamas also have the power? Hamas has a long record of firing those rockets from the vicinity of schools. It has sought to prevent ordinary Gazans from obeying evacuation orders, deliberately putting them at increased risk. It hides in a vast network of tunnels while civilians must fend for themselves above ground.

The Israeli government and Hamas agreed on Wednesday morning to a four-day cease-fire in which Hamas would free 50 of the hostages. But Hamas did that only because it’s under intense military pressure. It could get a real and lasting cease-fire for the people of Gaza — and probably safe passage out of the territory for many of its members — in exchange for releasing all the hostages, surrendering its arms and renouncing its rule in favor of some other Arab power.

That Hamas has done none of these things isn’t shocking: It’s a terrorist death cult. What’s shocking is that people in the Cease-Fire Now crowd don’t appear to have much interest in making any demands of Hamas equivalent to those they make of Israel.

They want Israel to stop firing. But do you often hear them insisting that Hamas return the favor? They want Israel to provide Gaza with humanitarian relief in the form of electricity, fuel and other goods. But I haven’t seen those protesters in the street demanding that Hamas provide Israel with humanitarian relief in the form of immediately freeing all hostages. They claim to want a “free Palestine” for all its people. But I never hear them criticize Hamas’s dictatorship, or its contempt for the civil and human rights of its own people, or its members’ avowedly antisemitic boasts of slaughtering Jews.

There is a buried, unwitting compliment to Israel in this asymmetry — an assumption that, as a Western democracy, the Jewish state is susceptible to moral suasion, public shaming, or at least diplomatic pressure in a way Hamas and its patrons in Iran aren’t.

Yet that compliment is rarely accompanied with even a gesture of respect for Israel’s grief, or the legitimacy of its grievance with Hamas, or its need to keep its citizens safe, or even its right to exist as a sovereign state. Even when Israel’s notional right to self-defense is briefly acknowledged, every exercise of it is immediately deemed a war crime, whatever the evidence.

For Israelis, what “Cease-Fire Now” means is “Surrender Now.” No wonder they decline to heed the call.

What about for Palestinians — women, children and noncombatant men for whom the calls for a cease-fire are supposedly intended? Would they benefit? In the short term, of course: Palestinian lives would be saved if Israel held its fire.

But a cease-fire wouldn’t spare just civilians. It would spare, and embolden, the main fighting force of Hamas. It would also embolden terrorist allies like Hezbollah. That’s a virtual guarantee for future mass-casualty attacks against Israel, for ever-larger Israeli retaliation, and for deeper misery for the people of Gaza. No Israeli government of any political stripe is going to allow the territory to rebuild so long as Hamas remains in charge.

That gives a second meaning to “Cease-Fire Now”: Either a demand for Israel’s total capitulation, or a recipe for a perpetual cycle of violence between a terrorist group sworn to Israel’s destruction and a Jewish state that refuses to be destroyed. Whatever else one thinks of Israel, no country can be expected to sign its own death warrant by indulging those who, if given the chance, would annihilate it.

There are good intentions, if also ignorance and shortsightedness, among many of those demanding a cease-fire. But there is also the bottomless cynicism of others who accept, and even celebrate, Hamas as it uses living Gazans as human shields and dead Gazans as propaganda victories. The tragedy of these protests, like so many “antiwar” movements in the past, is that the naïve and earnest are again being manipulated as tools of the cunning and cruel.

Instead of Cease-Fire Now, we need Hamas’s Defeat Now. Only on that basis does a lasting peace for Israelis and Palestinians alike have any chance to follow.