“Who the hell was the impostor?” Trump railed after the New Hampshire primary against Haley, who acknowledged his victory but has refused to drop out of the Republican presidential nomination fight. “When I watched her in the fancy dress that probably wasn’t so fancy, I said: ‘What’s she doing? We won’.”

Haley, who lost in Iowa and New Hampshire but has vowed to stay in the race through her home state’s first-in-the-South Republican primary February 24, shot back that Trump threw a “tantrum” because he feels threatened.

“It’s not just that he’s running against Nikki Haley,” said Debbie Walsh, director of the Centre for American Women and Politics at Rutgers. “It’s because she’s even deigning to challenge him … He goes after women for their appearance, for their gender.”

In fact, Trump has bragged about dominating women, an assumption challenged when one refuses to step aside.

“You can do anything” to women when you’re famous, Trump said on the Access Hollywood tape that threatened his 2016 campaign.

And yet Trump defeated Clinton with 39 per cent of women voters casting their ballots for him. Trump’s share of women voters increased in 2020 to 44 per cent, even as he lost to President Joe Biden – in part because Biden gained support among men, according to a Pew Research Centre survey of people confirmed to have voted in those elections.

Haley, for her part, has mostly taken Trump’s sexism in stride. She told CNN on Sunday that he was respectful to her when she served as his ambassador to the United Nations, but now is “flawed”.

Hillary Clinton

She was a “nasty woman”, didn’t look presidential and her voice gave Trump a headache, according to Trump.

But the defining visual of Trump’s approach to Clinton, his Democratic rival in the 2016 presidential election, came at a debate October 9, 2016, in St Louis, Missouri, two days after The Washington Post reported the contents of the “Access Hollywood” tape.

As Clinton answered questions during the town hall-style event, the 6-foot-3 Trump repeatedly hovered over and behind the 5-foot-5 former senator and secretary of state. He loomed so close, she wrote later, “my skin crawled”.

During a rally in North Carolina a few days after the debate, Trump appeared to hark back to the moment. “When she walked in front of me. Believe me, I wasn’t impressed,” he said.

Nancy Pelosi

Trump as president called the House speaker, “Crazy Nancy”, refusing to shake her hand at the State of the Union address after the House had impeached him.

She called him worse things – questioning his “manhood” in one meeting with Democrats, “ as if manhood could ever be associated with him”.

In 2019, she issued a smirk-and-clap to him when he arrived to deliver the State of the Union speech, a moment preserved in an iconic photo.

The next year, she openly scoffed at him on-camera as he spoke. Then she ripped up a copy of his speech on-camera behind his back and held up the pieces for all to see.

Haley has stepped up her questions about Trump’s mental fitness since a January 19 speech when he repeatedly seemed to confuse her with Pelosi. She uses it to highlight her calls for mental competency tests for politicians – her way to highlight both Trump’s and Biden’s ages (77 and 81, respectively).

Kamala Harris

Trump barely mentioned Democratic Senator Tim Kaine when he was Clinton’s running mate in 2016. But four years later, the president had plenty to say about Biden’s vice presidential pick, Kamala Harris.

Trump almost immediately called her “nasty”, and said that “nobody likes” Harris. That comment taps into a common standard of likeability that is applied to women in leadership far more often than men.

He also told voters in North Carolina it would be “an insult to our country” if Harris became the first female president.

Liz Cheney

Former Republican congresswoman Liz Cheney of Wyoming continues to draw Trump’s wrath even after she lost her House seat in a primary last year.

Cheney was one of 10 House Republicans who voted to impeach Trump after the January 6 insurrection at the US Capitol building, and she’s declared it her mission to prevent Trump from returning to the presidency.

Doing so, she warned late last year, would mean the US could become a dictatorship. Trump called her: “Crazy Liz Cheney”.

Carly Fiorina

Trump mocked former Hewlett-Packard CEO Carly Fiorina’s appearance in a 2015 interview with Rolling Stone.

“Look at that face,” he said of Fiorina, who was then part of the field running for the Republican presidential nomination. “Would anyone vote for that? Can you imagine that, the face of our next president?”

Other women who get under Trump’s skin

No one rankles Trump quite like women who face him in court. Last month in New York, a judge threatened to throw the former president out of a courtroom for ignoring warnings to keep quiet while writer E. Jean Carroll testified that he shattered her reputation after she accused him of sexual assault in a Manhattan department store.

Trump’s mutterings during the proceedings – “it is a witch hunt” and “it really is a con job” – came while the jury was in the courtroom. Earlier, without the jury present, Trump could be seen slamming his hand on the defence table when the judge refused a request.

The drama culminated expensively January 27 when the jury said Trump must pay Carroll US$83.3 million for his social media attacks against her. That’s on top of a US$5 million sexual assault and defamation verdict last year from another jury in a case brought by Carroll.

Stephanie Clifford, better known as adult film actress Stormy Daniels, incensed Trump during legal proceedings stemming from a US$130,000 payment she received from Trump lawyer Michael Cohen to silence her about an alleged affair with Trump in 2006. Trump denied that and began calling her “horseface”.

On the campaign trail

Haley has carefully calibrated her candidacy as a woman.

She frequently references her high heels. She recalls defeating older, more powerful men on her way to the South Carolina governor’s office. And she talks about the need to raise “strong girls” into “strong women”.

That tack allows Haley to deflect Trump’s aggression, hitting back with a smile and letting her supporters draw their own conclusions.

Laura Schroder, a 39-year-old mother of three, brought her children to see Haley recently at a Mauldin, South Carolina, rally. “He’s very immature,” she said of Trump, “and so clearly scared to lose to powerful woman.”

Haley herself makes a similar argument, such as one jab to chide Trump for refusing to debate her.

“Man up, Donald,” she says, “I know you can do it.”