Watching Australian Prime Minister Julia Gillard's skewering of opposition leader Tony Abbott for his "repulsive double standards" and sexism, was to see a worm turn into a dragon.

Inspirational in her well-controlled wrath, she was like a latter-day Moses, handing down tablets for modern women engraved with the words: don't get mad, get even.

The misogyny Gillard has faced throughout her career shows what other high-fliers have to endure. Those who've famously been the butt of insults include Angela Merkel and Hillary Clinton – "iron my shirt!", someone yelled at her during a speech – but countless more are in the firing line too. In one case, Greek politician Ilias Kasidiaris threw a glass of water over a politician taking part with him in a television debate and then slapped the face of another. His pathetic excuse was that these middle-aged women had provoked him.

If it were only those in prime jobs who aroused prejudice and anger it might not be so scary. But when high-standing, articulate women are harassed by men of equal stature, it tells you how deeply entrenched sexism is. One can only imagine what those on the lower rungs of the social ladder have to go through. Actually, we don't have to imagine, given the never-ending stories of criminal exploitation and intimidation at the hands of the likes of Jimmy Savile, or of pimps and rapists in towns like Rochdale. And, as Gillard showed, the problem is global. The light convictions handed down last week to men who serially gang-raped two young French women are beyond insulting. Yet they should probably come as no surprise, this being the homeland of Dominique Strauss-Kahn, who recently admitted his penchant for orgies and prostitutes was inappropriate for a politician though not for those in less public professions.

Meanwhile, influential, intelligent individuals who could help change attitudes sometimes appear to be working for the opposition. On the covers of their latest albums, for instance, Martha Wainwright poses naked and Diana Krall reclines in suspenders and basque. Singers do not need to flaunt their bodies to sell their music; it should speak for itself. The idea of Bruce Springsteen or Bob Dylan doing likewise is risible. Such displays reinforce the insidious, crippling and dangerous assumption that a woman's only value lies in her looks.

I want to believe that in her courageous speech Gillard has got the feminist message back on course, but chances are it'll change nothing. Increasingly, in fact, I wonder if society is not only as sexist as it was a century ago but, alarmingly, that it might be more so.

Feminists like myself could be certainly forgiven for fearing we have lost ground. In the 1980s and 1990s it was acceptable to be politically outspoken, to wear what we liked and vocally resist being belittled (or groped). Today's young women, however, treat feminism as if it was as old-fashioned and bad for their image as a pair of baggy dungarees. Thanks to better opportunities in education and at work, this generation has been lulled into thinking they are on an equal footing with men, and that the world is theirs for the taking. Unfortunately, it is not. If politicians like Abbott, on hearing that women are underrepresented in powerful jobs, can reply, "Is that a bad thing?", how far has women's cause really advanced?

The problem is, old-guard feminists are weary. We don't even seem to speak the same language as women half our age. Yet what's needed is for a new and youthful feminist movement to pick up the baton. If younger women want to live in a world where they are not mocked, overlooked or tyrannised simply for being female, they must take on the fight. It won't be easy, and it will be uncomfortable. But if each of them does no more than change the attitudes of people in their classroom, or family, or office, they will be helping to tilt the scales. Admittedly, few are likely to win a fan club of millions as Gillard just has. But then, a week before she launched her tirade, everybody thought she was meek and mousy. Now she's an international heroine – that's the difference a woman with her hackles up can make.