This month I decided that after over 10 years of waxing lyrical about feminism, it was about time I read some theory; and so I bought a copy of Betty Friedan's seminal tome, The Feminine Mystique, which was published 50 years ago this week.

"Feminine mystique" is the name Friedan coined for the impossibly perfect vision of the 1960s American woman: domestic goddess, devoted mother, available lover, faithful wife. The book angrily charts the lie that Friedan and her contemporaries were sold – that the battle for gender equality had been won, and all that remained was for women to enjoy the freedom of housewifery; the only thing that could ever fulfil them. Friedan repeatedly alludes to "the problem without a name", the term she uses for the malaise felt by the women experiencing this oppression and being told it was happiness.

There are some valid criticisms of The Feminine Mystique – like the fact that Friedan only refers to working class women when suggesting they could act as nannies to alleviate the ennui of middle-class housewives – but it's still a pivotal and revolutionary work. When I read it, I could almost see those women looking down at their wrists and seeing chains materialise, chains that had previously been invisible to them. The New York Times this week carries several letters from elderly women to whom reading Friedan's work was a life-changing experience.

To my mind, the most amazing and miserable aspect of The Feminine Mystique is how relevant it still is. Women of my generation are still being sold lies to keep us obedient. We are told that we are valued, until we accuse a revered man of rape. We are told we are equal, and yet we still do most of the low-paid and unpaid work. We are told we are respected, and yet we are harassed in the street, objectified and ridiculed in the media, and haunted by words like nag, harridan and hysteric in our personal relationships. Like Friedan's, our feminism is stifled by the belief that the battles have been won, and we are free to enjoy equality in all of its male-sanctioned glory.

There are the flickers of a revival of feminism: slut walks, projects about harassment and media objectification and feminist summer schools all suggest a new generation of women fighting the lies that they are being sold. But at the same time, the pole-dancing, one-of-the-lads brand of feminism which was such an utter failure in the 1990s seems to be re-emerging in a different form.

Perhaps, then, contemporary feminism is at a crossroads: for every feminist summer school, we have Caitlin Moran's swashbuckling, blokey feminism, which seems to be about making lots of witty observations about sexism, without ever putting them in the context of social oppression. For every campaign against objectification, we have the Sex and the City brand of feminism, as personified by a burgeoning movement in America calling itself "sexy feminists", which reassures us that one can believe in gender equality and still pay hefty sums of money to have pubic hair ripped out at the root.

In my mind, if being sexy and funny are the two cornerstones of a new feminist movement, we may as well all pack up and go home now. At its core, feminism should be angry. It should be angry because women are still being taken for a ride. Like the women in The Feminine Mystique, we are being sold a lie of equality in a society where the odds are politically, socially and economically stacked against us.

Feminism's most basic function should be to emphasise that sexism is not an accident, but an inevitable consequence of a society structured to favour men. Jokes about vaginas and reassurances that we won't have to give up lipstick are not enough. To put it bluntly, a new feminism should not be afraid to piss people off.

Sexy, funny feminism is inspired by the fear that feminism will never get anywhere unless it is likeable. For a long time now, feminists have been told that their message will never spread to the masses if the messenger appears to be an angry man-hating lesbian shouting the odds from a gender studies seminar room. But we need to realise that popular, non-threatening feminism is destined for failure as well. In a patriarchy – and if you are a feminist, you accept that we are living in one – what is popular and non-threatening is what men deem to be acceptable.

When feminists decide they want to appeal to everybody, what they are really doing is attempting to appeal to men, as culture in a patriarchy is defined by male values and male norms. Feminism that prioritises popularity over its own integrity will necessarily fail, as it is bound to reproduce the very problems it is fighting against. Perhaps Moran's recent observations that women who wear high heels are inviting rape are testament to this.

Friedan changed feminism because she wrote a book that spoke to women's hearts and souls, and wasn't afraid of offending men in the process. An 82-year-old woman wrote in the New York Times this week that The Feminine Mystique had made her realise that she was "not a freak" for feeling a sense of malaise. Women today are becoming angry at being made to feel like freaks for feeling malaise at being cat-called, objectified and shamed. The goal of feminists must be to harness that anger to create something better, not stifle it with a feminism which pleases everybody but changes nothing.