ANY notion that sexism is dead and buried was dispelled last week, following a passionate speech by Australian prime minister Julia Gillard.

Responding to opposition leader Tony Abbott's call for the Speaker to resign for sending sexist texts, Gillard said that if Abbott wanted to know what misogyny looked like he should pick up a mirror.

"I will not be lectured about sexism and misogyny by this man," she said. "Not now, not ever." And so she continued – for 15 excoriating minutes – listing his transgressions, which included standing outside Parliament next to a sign that read: "Ditch the witch." "I was offended," Gillard added, "when the leader of the opposition stood next to a sign that described me as a man's bitch." Then there was his advice, during his carbon pricing campaign, on "what the housewives of Australia need to understand as they do the ironing".

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Gillard's performance was that of a woman who had had enough, not just of Abbott, but of the bile-spouting media and blogosphere, and who finally wants to call a spade a spade.

There's no escaping the truth of Gillard's accusations. That slogan, "Ditch the witch", reeks of old-fashioned misogyny. But even more significant than Gillard's words was the response they provoked. "I almost had shivers down my spine," said Sara Charlesworth, an associate professor at the University of South Australia – and she was far from alone. Within hours, the speech had gone viral on the internet, becoming the most watched Australian political video of all time.

That a political commentary could set the web ablaze shows the extent to which it chimes with real feelings. Gillard's speech itself seems to have offered up a mirror in which many women see their own frustrations. It has tuned into a pervasive discomfort and anger. In the United Kingdom, for instance, we are having our own moment of introspective soul-searching, questioning how the sexual abuse of young girls by a male celebrity, Jimmy Savile, might have been so thoroughly ignored – what climate could have led so many in institutions to turn a blind eye? That seemingly old-fashioned word, patriarchy, has come back into currency. Writers have regaled us with tales of gropings and lewd comments that suggest that a boys'-clubbish sense of entitlement has endured, despite the advances achieved by the women's movement.

Meanwhile, a tirade against sexism by a female in power is long overdue. Women may have seized the political reins in many countries over the last five decades, but this is the first time a leader has so thoroughly tackled the elephant in the room. So far, it has been considered weakening to do so, as though the mere mention of sexism might remind the public that the speech-maker is a woman and therefore destroy her credibility. In the USA, during the 2008 presidential race, many were disappointed that Hillary Clinton did not make such a "gender speech", and had failed to deliver her own equivalent of Barack Obama's "race speech".

Indeed, if anyone understands Gillard's frustration about the onslaught of media misogyny, it is surely Hillary Clinton. The sexism she has endured over her career, and particularly during that presidential race, has been well

documented. Betsy Reed, writing in The Nation, summed it up: "She's been likened to Lorena Bobbitt [who castrated her husband], a hellish housewife, described as witchy, a she-devil, anti-male, a strip-teaser. Her loud and hardy laugh has been labelled the cackle, her voice compared to fingernails on a blackboard. And as one Fox News commentator put it, when Hillary Clinton speaks, men hear take out the garbage."

Clinton has also been at the receiving end of the message that her job is really to do the ironing. As she delivered a speech at a New Hampshire caucus, one man stood up screaming: "Iron my shirt!"

Some might argue that Gillard, and Clinton, were victims not of sexism but simply of the culture of infantile name-calling with which all politicians, regardless of gender, are currently assaulted. It is just, they might say, a symptom of our rude times. But the political persecution to which Gillard has been subjected suggests otherwise. According to Australian writer Anne Summer, Gillard has been undermined in a way that is deeply gendered and highly personal, by both the opposition and the media. "There is an entire industry of vilification," writes Summer, "much of it sexually crude, all of it offensive and designed to undermine her authority and thus her legitimacy in the role as Australia's first female prime minister."

Ironically, female leaders of the past were actually protected from such insults and jibes by traditional patriarchal attitudes of respect towards females. In the old days, men didn't think it was decent to lay into a woman. Describing the 1950 senatorial race in California in his book Tricky Dick And The Pink Lady, Greg Mitchell writes that when US Republican Richard Nixon came up against Democrat Helen Douglas, he was warned: "You can't get into a name-calling contest with a woman. The cost in votes would be prohibitive."

Meanwhile, it seems the UK's political culture is not so very different from Australia's. Kate Green, the Labour MP who campaigned to have Top Totty blonde beer removed from a House of Commons bar, is one of many to applaud Gillard's daring speech. She has long been shocked by the sexism exhibited in Parliament. Top Totty (whose beer tap shows a cartoon of a scantily clad woman) was, she says, just one symptom of a culture where the normal kind of respect you would expect in the workplace didn't apply.

She lists other examples of this culture at Westminster. There was the time thirty- something MP Stella Creasy was told to get out of a Members-only lift, because a junior minister assumed she was a researcher. Then there was David Cameron's prime ministerial ticking-off of Angela Eagle, whom he told in the House of Commons to "calm down, dear".

Here in Scotland, there have been notable instances of lamentable sexism. Most memorable, perhaps, was the case of former MSP Frank McAveety, who in 2010 was caught on microphone ogling a 15-year-old during a Parliamentary committee meeting he was convening, describing her as "very attractive ... dark and dusky" and adding: "We'll maybe put a wee word out for her." At the time, MSP Sandra White complained that he was not immediately sacked (he later resigned). Today, White notes that it is not only older men like McAveety who are guilty of such attitudes, but also "the younger generation brought up on lads' mags".

"A lot of the time the men are very subtle about it," she says. "It's wee remarks that slip out. I think it's harder to pinpoint than it used to be, but it's still there and it's deep down. For instance, in the Scottish Parliament if a woman is making a speech and is perhaps not at the top of her game, men often interrupt and intervene in a way that they wouldn't if a man was performing in a similar way."

Meanwhile, the surge of reaction to Gillard's speech suggests these attitudes are not confined to the field of politics but all-pervading. Five months ago, Lauren Bates set up a website called The Everyday Sexism Project and has since collected 8000 entries by women recording their own experiences at work and in their personal lives. She believes sexism is "incredibly widespread" across British society, and in all kinds of workplaces. She notes, for instance, that she has seen the same complaint – of a manager groping a female employee's bottom – from both a burger restaurant and a "big City financial firm". The stories logged by the project range "from small snide comments, like being called a sweetie or asked by a male staff member to make the tea, to inappropriate sexual comments at board meetings and actual sexual assault". By documenting the smaller, subtle grievances as well as the darker, more serious instances of sexism, Bates's project reminds us of the way women are routinely infantalised.

Bates is particularly concerned about the message conveyed to young women about what they might have to deal with if they choose a career in politics. "The treatment female politicians receive sends damaging messages to young girls, discouraging them from going into politics and thus perpetuating the cycle," she says. On her site, one woman describes being part of a group taken round the Houses of Parliament, which ended at the Commons shop with the guide commenting: "There are recipe books for the girls."

Bates does not, however, believe that this is about blaming individual men. "It's just an attitude that's normalised in our culture," she says. "And the problem is that women feel this is the way it is and that they just have to put up with it. You can see this normalisation in small verbal expressions. Many women, for example, find it frustrating to be referred to as 'the girls'. Conversely, many talk of the existence of a 'boys' club' mentality'". Sexist behaviour is talked of as an open secret, and in that climate, she says, "it's very hard to be the one who speaks out".

After Bates talked recently on the radio, she received an email from a man objecting that "there isn't any sexism any more". But the reception of Gillard's speech suggests this is not the case. On the surface we like to present ourselves, in spite of statistics of economic inequality, as a society of equality, in which sexism is just an ironic joke. Yet, several decades into the feminist movement, sexism still seems like an obstinate, unlanceable boil.

While it may be true that Gillard's speech needs to be seen against the backdrop of political manoeuvring in which it was made, her attack on Tony Abbott comes across as heartfelt. It's as if she can no longer bear the hypocrisy that surrounds her.

And many people back her up. Last week, Senator Christine Milne of the Australian Green Party declared that every female parliamentarian experienced sexism. As for Abbott's sexism: "Half the time I don't think he even realises it," says Milne. "He epitomises the hyper-masculine style of male politicians - and he trades on that. His attitude to women is very much of the male dominated, male protection, the father looking after the women as very much the secondary players ... and no amount of bringing his wife into the public arena is going to change people's perception of the kinds of remarks he makes."

After a week that saw the Taliban-ordered shooting of a 14-year-old girl who had spoken out about attacks on female schooling in Pakistan, these political cat-callings may seem to be of scant significance within the global scheme of women's rights. But they are not disconnected. Both situations are the result of cultures which are trying to keep women out of power. They are symptoms of – and here's that old-fashioned word again – patriarchy. In Australia, clearly, that culture is failing. The boys' club is losing some of its stranglehold – and Gillard's attack is a sign of that. It is a declaration of confidence as well as anger.

When a female leader can stand up and call sexism for what it is, rather than pretend it does not exist, then progress is truly being made. When she can say, "I am offended", and not feel the need to temper her opinion in order to appeal to men, we are taking a step forward.