If there were a Nobel Prize in Winding the US President Up, it would have to go to the self-proclaimed patron saint of shade, Nancy Pelosi.

Nobody manages to burn him so often or annoy him quite so intensely as the speaker of the House of Representatives. At a time when Donald Trump’s Twitter tantrums have ratcheted up to become almost an hourly occurrence, that’s quite an achievement.

The pair’s latest altercation came after a contentious meeting about Syria on Wednesday afternoon, at which Trump and Pelosi traded insults and she ended up walking out. Trump’s less-than-killer barbs are said to have included “I hate Isis more than you do.”

He also called the California Democrat a “third-grade politician”. (Initial reports suggested he said “third-rate”; she later clarified that it was in fact the more infantile “third-grade”.) Trump was chastised for this by the House majority leader, Steny Hoyer, who suggested such insults were not useful.

As entertaining – or terrifying – as all this might be, it ultimately works in Trump’s favour

Speaking to reporters later, Pelosi said: “I pray for the president all the time, and I tell him that. I pray for his safety and that of his family. Now we have to pray for his health, because this was a very serious meltdown on the part of the president.”

Trump responded by doing what he always does when he’s feeling under attack – something that seems to be happening with increasing regularity. He went on a Twitter rant. One of his posts featured a photograph of the meeting, along with a characteristic playground insult. “Nervous Nancy’s unhinged meltdown!” he wrote.

In the photo – as revealing a study of the deep divisions in Washington, DC, as any Renaissance composition – Pelosi looks anything but nervous. She looks powerful, angry and intimidating.

She is standing with her body tilted slightly forward and her finger pointed across the table at Trump, whose chair is pushed back a little from the table, in a defensive posture, his expression crumpled in outrage. Four of the five people sitting alongside him look chastened and unhappy, their faces a series of studies in hangdog mortification.

Nancy Pelosi needs help fast! There is either something wrong with her “upstairs,” or she just plain doesn’t like our great Country. She had a total meltdown in the White House today. It was very sad to watch. Pray for her, she is a very sick person! — Donald J. Trump (@realDonaldTrump) October 17, 2019

When Trump attacked Pelosi on Twitter in June 2016, writing, “Obama just endorsed Crooked Hillary. He wants four more years of Obama – but nobody else does!” Hillary Clinton responded with the social-media version of a mic drop, telling him: “Delete your account.” Within an hour it had become her most retweeted post ever.

Pelosi went one better yesterday. She made the photograph Trump tweeted the cover image for her Twitter and Facebook profiles. In this she may have taken her inspiration from Greta Thunberg, who, after Trump tweeted mockingly about her appearance before the United Nations – “She seems like a very happy young girl looking forward to a bright and wonderful future. So nice to see!” – turned the insult around and temporarily adopted his words as her Twitter bio.

“A very happy young girl looking forward to a bright and wonderful future,” it briefly read.

In case Pelosi’s move went unnoticed, her deputy chief of staff, Drew Hammill, tweeted about it. “Thanks for the new cover photo @realDonaldTrump!,” he wrote.

For all that Pelosi is the saint of shade, Trump is the master of distraction

As usual, the Twitter war sparked support, indignation and childish insults on both sides. But as the Washington-based website the Hill tweeted, “This photo could be a Pelosi campaign poster – the sole woman in the room, literally standing up to the President. Why he thinks this makes her look bad is a mystery.”

This is at the heart of why she annoys him so much. She is not just the “sole woman in the room”; she is a powerful, intelligent woman who is unafraid to show her anger – all things bound to wind up a man who prefers his women silent, decorative and, preferably, somewhere else.

Pelosi’s form when it comes to goading Trump includes the comment that the border wall is “like a manhood thing for him – as if manhood could ever be associated with him”.

She is also said to have remarked to an aide that talking to Trump is like a tinkle contest with a skunk. “You get into a tinkle contest with a skunk, you get tinkle all over you.”

During his state-of-the-union address last February she launched a thousand memes when she interrupted his rambling to stand up and deliver a slow handclap.

After social media anointed her the “patron saint of shade” she began selling T-shirts and tote bags emblazoned with the words and a caricature of her clapping in her online store.

But as entertaining – or terrifying – as all this might be, it ultimately works in Trump’s favour, providing yet another diversion from the things he’d rather American voters didn’t notice.

For all that Pelosi is the saint of shade, Trump is the master of distraction. And there’s nothing like this kind of sideshow to draw public attention away from the long – and getting longer by the day – list of things he’d rather everyone forgot about: Turkey, Russia, Ukraine, the impeachment proceedings.

Pelosi may have won this particular social-media spat. But it’s far from clear who’ll win the much bigger battle still to be fought.