After urging Australians to vote for “the one with the not-bad-looking daughters” and appointing one woman to his 19-member cabinet, Tony Abbott provoked mirth and dismay today by giving himself ministerial responsibility for women’s issues.

“Why do I suddenly feel like I cannot breathe?” tweeted a prominent feminist writer, Jane Caro, after Mr Abbott was sworn in as Prime Minister and his additional portfolios were disclosed. “It’s a joke, right?” asked one woman on Twitter.

This, after all, as some commentators noted, is the man who railed against the impact of rising electricity prices on “the housewives of Australia … as they do the ironing”; who suggested men were “more adapted to exercise authority or to issue a command”; and who urged the former Prime Minister Julia Gillard (who lives with her partner) to “make an honest woman of herself”.

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Ms Gillard is best known overseas for her speech last year accusing Mr Abbott of serial sexism and misogyny. Following that speech, the then opposition leader made determined efforts to revamp his image and portray himself as female-friendly.

His wife, Margie, rejected the notion that “somehow Tony doesn’t get women”, and revealed he is a “softie” who cries in soppy films. His chief of staff, Peta Credlin, told how he supported her during her attempts to conceive via IVF – even storing her fertility drugs in his parliamentary fridge.

During the election campaign, Mr Abbott was rarely seen without one, often two, of his three adult daughters. Whenever he committed a faux pas – telling girls in a school netball team that “a bit of full body contact never hurt anyone”, for instance – a daughter would be on hand to dismiss it, light-heartedly, as a “daggy [uncool] dad moment”.

Many women remained unconvinced. And for them, this week started badly and got worse. First came the announcement that Julie Bishop, the Foreign Minister, was to be the sole female cabinet member. Ita Buttrose, a veteran journalist, spoke for many when she declared: “You can’t have that kind of parliament in 2013. It’s unacceptable.”

Then the Prime Minister added insult to injury by asserting – in comments viewed by some as deeply patronising – that the number was bound to increase, because there were “some very good and talented women” in his conservative coalition.

Today critics of Mr Abbott – who insists that all ministerial appointments are made “on merit” – were digesting the news that, along with indigenous affairs and national security, he has assumed personal responsibility for “women’s policies and programmes”. He wants to “ensure that these key whole-of-government priorities are at the centre of government”, he explained.

Almost as appalling, to some, was the news that he will be assisted in the women’s portfolio by a junior minister, Michaelia Cash, best known for a scathing attack in parliament earlier this year on Penny Wong, Ms Gillard’s Finance Minister.

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After Ms Gillard was deposed by Kevin Rudd, Ms Cash denounced Ms Wong – who had supported Mr Rudd’s move – as being part of a “sisterhood stabbing one of their own in the back”. Making clawing and stabbing motions, she accused Ms Wong of “drinking from the chalice of blood”.

One blogger circulated a list of “things that have more women in them than Tony Abbott’s cabinet”. They include the Afghan government, the US Supreme Court, the Iranian cabinet, a staff meeting of the men’s magazine Zoo Weekly and the Saudi Arabian Olympic team.

Lady justice: His record thus far

Abortion

While he has called abortion “the easy way out”, he said in June: “I make it crystal clear the coalition has no plans for change in this area [abortion law], none whatsoever.”

Female quotas and affirmative action

He, and his Liberal Party, oppose them in politics and business. “Personally, I’ve always been cool on quotas,” he said in 2011, adding: “If women are given the chance to show their abilities, they will get places on their merits.”

Paid parental leave

He plans a scheme where parents will receive the equivalent of half their income – up to A$150,000 (£87,795) – for six months. Critics say it is too costly.