They’re both fond of wearing bizarre makeup. Both face legal jeopardy at home, and they both took part in an illegal attack on Iran. Like the “brothers in arms” the Israeli leader wants the US president to think they are, Donald Trump and Benjamin Netanyahu appear to bicker like siblings.

This is an appearance. Not reality. The relationship between the two leaders has been closer to that of an agent and his handler. It has always been “Bibi” who’s done the handling, and it is always The Don who has been handled. This has delivered unimagined benefits to Netanyahu, who, with the help of Trump acting against the advice of his own band of court loyalists, has reduced the US to a protector of Israel.

In his latest and most venomous swipe at the Israeli prime minister, Trump has reportedly said Netanyahu is “f***ing crazy” because of his apparent desire to apply the military doctrine that he used to flatten Gaza in the context of his new assault on Lebanon – a policy that, without doubt, will result in the mass evacuation of civilians.

Trump has used vulgarity in describing his frustration with his fellow “wartime leader” – a term he loves to use – but not because the destruction of Gaza was immoral and provoked accusations of genocide against Israel. He is angry because Israel’s war in Lebanon jeopardises his own attempts to get out of the joint US-Israeli campaign in Iran. Tehran’s leadership has refused ceasefire talks while Israel continues to bombard Lebanon, and refuses to rein in its proxy force there, Hezbollah.

Trump officials reportedly told the Axios news site that the US president had yelled at Netanyahu: “You’re f***ing crazy. You’d be in prison if it weren’t for me. I’m saving your ass. Everybody hates you now. Everybody hates Israel because of this.”

A counter-briefing from Israel pushed back on the accuracy of the reference to prison, but felt no need to remonstrate on the accusation of madness.

Netanyahu has been indicted by the International Criminal Court (ICC) for crimes against humanity. In response, the Trump administration imposed sanctions on at least nine senior ICC staff members, and accused the international war crimes tribunal at The Hague of being a threat to national security.

In simple terms, Israel’s leader has been protected by Trump – no matter the international reputational damage to the US.

It is the domestic courts that Trump is referring to, though, when he talks of keeping Netanyahu out of jail. Netanyahu is on trial on a range of corruption charges. His cross-examination has frequently been postponed because of the conflicts Israel is locked into. If the reports of what Trump said to him are true, Trump is admitting that the attack on Iran was a personal favour to the Israeli leader.

Netanyahu failed to persuade previous US administrations, under George Bush, Barack Obama and Joe Biden – all supporters of Israel – to attack Iran. None of his predecessors were convinced by Israel’s claims that Tehran was “two weeks away” from developing a nuclear weapon, or posed an existential threat.

Mysteriously, though, Trump went on to accept Netanyahu’s war plans in February this year, without any idea of what “victory” would look like.

Trump’s performative rage against Israel first emerged after the Hamas offices in Qatar were hit by rockets last September in an incident that prompted a public apology from Netanyahu.

“We basically have two countries that have been fighting so long and so hard that they don’t know what the f*** they’re doing, do you understand that?” said Trump of Israel and Iran. “I’m not happy with Israel.”

The latest outburst against “f***ing crazy” Netanyahu is largely rhetorical.

There are only two other men in the world that mesmerise the US president in the same way: Vladimir Putin and Xi Jinping. Whenever Trump meets with either of them, it appears he has been seduced into agreeing with their respective claims to Ukraine and Taiwan. They have the appeal of being modern imperial figures. Proximity to their level of authoritarian power inspires Trump, and he pursues the same in his own country.

Netanyahu’s hair is dyed a distracting shade of intense purple-blue. He wears a thick layer of foundation at all times, to optimise his appearance on TV. So he and Trump are both vain. But Netanyahu’s voice is deep, and his background is macho. He is a former special forces soldier, and his brother, Yoni, is a national war hero.

Standing with “Bibi” gives Trump an ego boost (and manliness by association).

Netanyahu knows this. He also knew earlier this year, when he sold the idea of war against Iran at the White House, that Trump was facing indictment if the Republican hold on Congress was broken in the midterm elections in November.

A war to end Iran’s nuclear programme, rescue Iranians from a theocracy, and remove Iran’s capacity to threaten Israel could boost Trump’s standing in the polls – in theory. The fact that this was unlikely did not matter; it just needed to appeal to the victim of Netanyahu’s manipulations, Donald Trump.

In April, a Pew Research poll in the US found that 60 per cent of Americans had an unfavourable view of Israel – up by 20 per cent in four years. With an eye on the midterm elections, this puts data behind Trump’s claim that “everybody hates Israel because of this [war in Iran/Gaza]”.

It is important to Trump that he does not appear to be a patsy for Netanyahu. And, as the manipulator in this relationship, Netanyahu has no problem with that.

The US president said in May: “He’ll do whatever I want him to do.” Whatever Trump may say, the truth is the other way round.