In her desire to shock and to embrace the limelight, Germaine Greer could give Lady Gaga a run for her money. Her performance on the BBC1's Question Time was a flamboyant slaying of a dragon that the rest of us call parental love.

"Little girls learn to flirt with their fathers," said Greer, with lofty contempt. "You know: 'Kiss daddy goodnight' and all this sort of business." The pain and bewilderment of the father in the audience – "That is an awful thing to say" – was shared by many viewers. This Circe of Question Time was casually poisoning the loving relationship between fathers and daughters, by making it part of the debate on the sexualisation of girls.

David Dimbleby asked her why she regarded the relationship as unnatural and she turned to him in triumphant disdain. She had never used the word "unnatural". Only he had.

The way in which we respond to Germaine Greer gives our age away. Those of us who remember Greer in her prime of influence respect her as an old warrior. My daughter's generation regard her as a mysterious relic. Her analysis of the female plight makes no sense. Young women can kick ass if they need to, but most of the time their relationships with men have never been easier. Female oppression feels as distant as slavery.

Where there is injustice, they tackle it with spirit and style. The SlutWalk is the expression of a new marketing-savvy style of feminism, rather than a civil rights movement. The issue of rape may be grave, but the approach is Facebook friendly.

As for girls flirting with their dads, the notion provoked gasps and pantomime retching when I tested it out. Germaine Greer regards the family as an oppressive, patriarchal institution. But things have changed since the Edwardian era. The modern Western family is as rights-based as the UN. Also, the internet generation has a much wider network of influences. Its main cultural reference for fatherhood is not an austere figure in his study, but Homer Simpson. Dads are human, loveable, ridiculous.

If you want a convincing portrait of a contemporary father-daughter relationship, it is no good looking to Greer, who is perhaps thinking of King Lear or her own unsatisfactory father. Much more accurate is the 19-year-old playwright Anya Reiss, whose latest work, The Acid Test, examines the dynamic between three young female flatmates. The clever, prudish one brings her father to stay after he has been thrown out of the home by his wife. The girls ply the father with alcohol and end up drunkenly riding him round the flat as if he were a horse. He is a cause for merriment and sympathy.

There is always a risk of hubris when you decide to put yourself at the head of a movement. Leaders are temperamentally prone to egotism and megalomania, Greer more than most. Her main fault, particularly serious for an academic, is her disregard for empirical evidence. She simply takes her own experience, and applies it to everyone else. At least Tracey Emin, another brilliant show-off, does not try to generalise her own life.

Greer is now in her seventies, living among hens and bluebells. The environmental protester Tamsin Omond or Anastasia Richardson, the 17-year-old, don't-mess-with-me organiser of the London SlutWalk, photographed in the Evening Standard in a floral dress and Doc Martens, are more reliable on up-to-date currents of feminist opinion.

Both these young women seem to have more in common with the suffragettes than with 1960s feminists. They favour high-visibility stunts, rather than Greer's self-referential arguments. They are activists, whereas Greer was ... well, always Greer.

Contemporary feminists are not trying to define themselves in relation to men; they are more concerned with women. How should women achieve equal pay, the balance of maternity leave and childcare, the effect of cuts on women's services? They are not tormented by little girls wearing pink. They do nor rail against the power imbalance of the vagina and the penis.

The SlutWalk refers to a crass remark by a Canadian policeman that women should not dress provocatively if they wish to avoid rape. But it is not a protest against men; it is about the rights of women to walk freely. As far as Greer is concerned, everything is about men. Her life has been dedicated to slugging it out with them. I suspect she prefers male company to women. She used revealing language in her Question Time attack on the cultural conditioning of girls. She said girls should not be "coy and manipulative" because "we would like them to be good chaps". She referred to her old-fashioned "boyish feminism" rather than the new girlish kind.

Greer once said that women were incapable of holding a civilised conversation at dinner, turning everything into a private quarrel. She added that hostesses generally dreaded wives. She is used to the wood-panelled, masculine atmosphere of high table, and is happy there. Her argument is really that of Henry Higgins: "Why can't a woman be more like a man?" Even her lustful book on beautiful boys is Audenesque in its tone.

All feminism is personal, and Greer's is bound up with being intellectual, Australian, a tomboy and childless. Of course the father in the Question Time audience was horrified by the suggestion that his daughter was flirting with him. To him, this was real life. To Germaine Greer, it was only of academic interest.

And yet we dismiss Greer at our peril. My generation of women, who came after Greer, were like John Major to her Mrs Thatcher. We were technocrats, rather than ideologues. Have women advanced much as a result? The world is still run largely by men for men. I reckon we still need a fearless, offensive Aussie shouting her mouth off. We should hold in reserve her angry proposition: If you can't join men, then you might as well beat them.

Sarah Sands is deputy editor of the 'London Evening Standard'