Antony Blinken spelled out the paradox when he spoke in Washington on Tuesday. Despite the rapidly escalating rhetoric, and the clashes along the Israel-Lebanon border, the US secretary of state insisted: “I don’t think any of the potential belligerents actually want to see a war or conflict spread. I don’t believe Israel does. I don’t believe Hezbollah does. Lebanon certainly doesn’t because it would suffer the most. I don’t believe that Iran does. and yet you have momentum potentially in that direction.”

This week, the Israeli foreign minister, Israel Katz, said a decision on an all-out war with Hezbollah was coming soon, and generals said their plans for an offensive into Lebanon were signed off. Hezbollah published drone footage of Israeli sites including key infrastructure in Haifa, and its leader, Sayyed Hassan Nasrallah, warned of a war “without rules or ceilings”.

The past eight months have shown that the parties are calibrating their deeds even as they ratchet up their words. and yet the prospect of a large-scale war has grown. Mr Blinken identified the risk as miscalculation. The deeper danger may be the momentum generated by the clashes, which have slowly but steadily escalated, with each side coming to see a greater conflict as inescapable. For many residents in northern Israel, the horrors of the Hamas raid on 7 October made continuing to live with Hezbollah on the doorstep unthinkable. Since then, Hezbollah has shown it can threaten Israel over an extended period at relatively low cost. On Hezbollah’s side, holding back may give Israel more time to prepare an assault.

Tens of thousands of people have already fled their homes in Lebanon and Israel; dozens have been killed, in addition to hundreds of Hezbollah fighters and more than a dozen Israeli soldiers. Israel has reportedly told the US that it plans a lightning attack. Its confidence that it can get out as easily as it gets in is startling given its own record in Lebanon. It has failed to achieve Benjamin Netanyahu’s declared goals in Gaza – the elimination of Hamas and the return of hostages – eight months and a reported 37,000-plus Palestinian deaths after it took on a far less experienced and less well-armed foe. It would face war on two fronts (not counting Houthi attacks in the Red Sea), with Israel Defense Forces troops who have spent months fighting in Gaza. The rift between the Israeli prime minister and the army is increasingly public: this week the IDF spokesperson Daniel Hagari said bluntly that “Hamas is an idea” and cannot be destroyed, adding: “The political echelon needs to find an alternative – or it will remain.”

An end to the war in Gaza may offer an off‑ramp in the north. But it cannot be depended upon. Each party has a reason to avoid further escalation. Hezbollah’s status is enhanced by the current situation and Iran does not want to squander a deterrent against an attack on its nuclear facilities. Lebanon is on its knees already. A full-scale conflict would be an existential risk to Israel itself in a way that the invasion of Gaza was not, with the US warning that its missile defences in the north could be overwhelmed – reportedly echoing domestic concerns.

Mr Netanyahu doesn’t listen to the Biden administration. He has smashed through its red lines and went out of his way to pick a fight with it this week. But the situation is unsustainable – and diplomacy, not war, must be the answer.