Over the last days, Tony Abbott’s been roundly denounced over the gender composition of his cabinet. No doubt he’s rather pleased.

It’s not simply that, with a few exceptions, the critiques came from progressive commentators who were duly forced into the untenable position of (at least implicitly) talking up conservative women they utterly despised. If you are on social media, you likely received memes about the female deficit in the Abbott government from the same friends who sent you incessant updates leading up to the defeat conceded this morning by Sophie Mirabella, a woman otherwise destined for cabinet.

More importantly, these attacks entirely reinforced the tropes on which Abbott fought and won the election: "vote for us and put the adults in charge". That was, more or less explicitly, the conservative pitch – a promise to restore stability after the Rudd-Gillard shenanigans. But a gendered undercurrent was never far from the surface. The natural order in the household required daddy to come back home; Abbott, a man’s man, would fix the mess created by that shrill feminist and the effete bureaucrat who replaced her.

To put it another way, Abbott quite overtly took on a certain kind of liberal feminism over the last year – and comprehensively defeated it.

Gillard’s misogyny speech, which was directed against Abbott, went viral. Yet, even as US sites such as The Huffington Post and Jezebel lauded the feminist PM from Down Under, Abbott’s position continued to improve, as Gillard’s polling became terminal.

Abbott was called out again and again on sexism: for his quip about the "sex appeal" of his candidate Fiona Scott, for the sleazy showcasing of his "not bad looking" daughters and other supposed gaffes. But Scott’s popularity skyrocketed, and the Abbott offspring were front and centre at Liberal victory party, parading in virginal white. Which is why Abbott probably does not particularly mind if, in his first weeks of government, he’s once more in the papers as the champion of traditional gender roles.

Tony Abbott, his daughters Bridget and Louise and wife Margie arrive for his swearing in ceremony. Photograph: AAP Image/Alan Porritt Photograph: /AAP

It’s not that opposing sexism is futile, or that denouncing misogyny necessarily backfires. But if the left doesn’t understand the logic of culture wars, we are doomed to be defeated in them, again and again.

After all, the forecasts for more of these cultural skirmishes are on the agenda in the months to come, partly because Abbott (an admirer of Bob Santamaria) has form as a cultural warrior but, more importantly, because he heads a government put in power without an obvious mandate and governing in difficult circumstances.

In the polling booth, voters signaled their opposition to Labor far more than they showed any particular enthusiasm for the Liberals. In opposition, Abbott could weld together the disparate tendencies of the contemporary right into a formidable campaign – a visceral hatred for the ALP could unite social conservatives with Hayekian free marketeers. But in the lodge, matters become far more complicated, not least because on the stump he explicitly and repeatedly promised not to embark on the austerity and union-busting on which his backers now want him to get cracking.

During the Howard years, the conservatives perfected a strategy for precisely such circumstances: you pick a battle that’s relatively trivial in itself (and thus doesn’t commit you to anything as dangerous as, say, taking on the building unions) but that has broader thematic resonance. You stage your provocation on a theme in which there’s at least the potential of public support (nationalism, racism, family values for example) and you use that support to draw progressive pundits and activists into a debate about symbolism that seems to put them at odds with the bulk of the population, along the familiar lines of "arrogant cultural elites" versus "ordinary honest battlers".

Culture wars are mostly a bluff, since they rest on the ability of wealthy politicians or shock jocks to pass themselves off as representatives of the common folk. Thus Rupert Murdoch, media billionaire, takes daily to Twitter to blather about the perfidy of "elites" – and if you buy that, I’ve got a nice bridge in Sydney you might like to inspect.

Yet, if the right’s often successful with the culture wars, it’s because many on the left accept the underlying contours of the argument.

After all, you’re as likely to hear progressives as much as conservatives explaining that the population’s innately reactionary, that this is a country of "ignorant bogans" who form a natural constituency for rightwing demagogues. Think about the aftermath of the election and the Facebook posts and tweets shared by irate leftists: why, the outcome proved the utter stupidity of Australians, a collection of mouthbreathers too dumb to comprehend what Abbott would do to them.

That’s the backdrop to an increasing fascination among progressives for clashes among the political elite, not because of what these stoushes represent to the rest of society, but because change at the top seems more viable than change at the bottom.

Naturally, the disconnect between the left and the population duly becomes entirely self-reinforcing. In the last few federal elections, great swathes of the populace indicated a disengagement from the political process. It’s not so surprising if they extend that cynicism to a left that seems fixated by precisely the insider manoeuvrings they find irrelevant to their lives.

Does this mean that progressives should simply abandon symbolic debates to concentrate exclusively on bread-and-butter issues?

Not at all. Though a call for an exclusively material left can sound tremendously radical, all too often it’s still predicated on the same conservative image of Joe and Jane Sixpack, boorish drones indifferent to anything other than the wages in their pockets.

Symbolism undoubtedly matters – and sometimes it matters considerably more to the disenfranchised than to the comfortable. The apology about the Stolen Generation changed nothing in and of itself, but resonated deeply with many Indigenous Australians. Same sex marriage probably has more consequences for gay men or lesbians trying to live their lives in outer suburbs or country towns than those in queer-friendly urban centres.

The challenge for the left is not to abandon symbolism, but rather to fill symbolic reforms with real content – to turn, say, the enthusiasm for marriage reform into a broader campaign against homophobia in all its forms.

At present, Abbott might be quite happy to offer himself as the patriarch-in-chief. But that’s because the debates about misogyny in Canberra too often seem like arguments affecting two competing sets of politicians (and no-one much else), rather than a particular manifestation of a struggle in which ordinary working people are themselves inextricably engaged.

Abbott’s image as the embodiment of gender conservatism works for him only so long as he can present anti-sexism as the preoccupation of a tiny elect, irrelevant to the problems of the many. If, on the other hand, progressives can use debates over sexism in political life to discuss the oppression faced by women who don’t hold positions of prominence and power, Abbott’s persona suddenly pits him irrevocably against him the bulk of the population.

And, at that point, he loses.