Late last year I went to a conference session on sexism in the workplace. About 25 of us, mostly young professional women, sat around in a circle and swapped demoralising anecdotes about how the pay gap, motherhood, sexual harassment and oppressive gender expectations had impacted our careers. In terms of narrating these experiences, we were all on pretty much the same page. There was furious agreement that women are subjected to sexism in the public sphere, and that this is harmful to individuals and to society as a whole. Fantastic, I thought. We're switched on, we know what's what, and we're here together to talk about what we can do to fix things.

But as the focus shifted from describing the problem to proposing solutions, it was like watching a train derail in slow motion. What about mentoring, somebody said. What if we teach women to negotiate for higher pay? What if companies are encouraged to set targets for women in executive roles? What if we build a culture of open negotiation in our own workplaces, where women are empowered to ask for more flexible hours?

I shifted in my seat, waiting for someone to bring up public day care, or government-funded parental leave, or the proliferation of underpaid pink-collar jobs, or the economic devaluation of women's reproductive labour, or any of the issues that have historically been sites of feminist struggle. Nobody did, so I raised my hand to mention my sister, who is a part-time childcare worker. How would training women to ask for higher pay help her, as someone who earns a set award wage and has very little power to negotiate anything? How would professional mentoring empower her? How would her life be improved by quotas for women on boards?

A mildly uncomfortable pause followed. I ploughed on, motivated half by an immediate anxiety about filling the conversational gap and half by raw indignation. Shouldn't our demands be for universal changes to the structure of society that will help all women, I asked. There was a subdued murmur of assent, and a couple of women voiced agreement. But the matter was soon forgotten, and I spent the rest of the session in a state of tense disappointment.

• • •

A few weeks before I went to the conference, a student petition emerged from Cardiff University calling for the cancellation of a lecture on twentieth-century feminism to be given by Germaine Greer. The petition's author, Rachael Melhuish, objected to Greer's beliefs concerning transgender people: 'Greer has demonstrated time and time again her misogynistic views towards trans women, including continually misgendering trans women and denying the existence of transphobia altogether,' it reads.

Greer responded to the petition on BBC Newsnight: 'Apparently people have decided that because I don't think that post-operative transgender men are women, I'm not to be allowed to talk,' she said. 'I'm not saying that people should not be allowed to go through that procedure, what I'm saying is it doesn't make them a woman.'

In the ensuing debates, much of the conflict concerned whether calling for Greer's exclusion from the university constituted a threat to freedom of speech and, more broadly, whether the current culture of campus feminism is oversensitive or censorious. Commentators who disagreed with her views on the ontology and political valence of trans people's genders mostly didn't enter into explicit arguments about why, instead pointing out the obvious reality that trans people are subjected to severe discrimination and violence, and that Greer implicitly endorses the beliefs by which transphobic violence is normalised and excused. That is, they took issue with her opinions in a functional capacity, rather than directly engaging with them.

This was a pity, because teasing out the threads of ideological disagreement between Greer and the petition-signers is thoroughly illuminating if you can stand the sound of people shouting at each other from across a 45-year gap. Greer's belief that surgery can't 'turn a man into a woman' and the biological essentialism to which this commits her, is not just a hallmark of Second Wave feminism, but the very basis on which it sought to build a common movement. It's not some wacky metaphysical conceit she and many other feminists of her era happen to believe for no reason; it is, or historically was, invested with a tremendous amount of productive and positive meaning that made feminism possible as a project. Whatever criticisms of seventies feminism are warranted (I won't go through them because I don't have all day), it did achieve substantial progress for many women, partially enabled by this belief.

The burden of reproductive labour that has characterised women's oppression—sexual availability, pregnancy, birth, childrearing, housework, the constant threat of rape and assault—arises, on this account, directly from biological causes. It's not hard to see why the existence of trans people poses a challenge for Greer; if she accepts trans women as women