Some women don't want to become bishops. They don't even want other women to become bishops. That much is evident from records released by Church House, which show that women made up almost half of the lay people who voted against legislation to allow female bishops in the Church of England. Voting figures show that 33 of the 74 General Synod lay members who voted against the measure were women, most of them conservative evangelicals or members of the church's Anglo-Catholic wing. They had the support of another 2,200 women who signed a petition opposing reform.

It's hard not to react to these figures by asking why some women appear to be their own worst enemies. Why do they actively oppose what seems to be in their own interest? The General Synod vote runs against the current of history, which suggests that women are increasingly voting for politicians who favour equality, such as President Obama. Reactionary positions on abortion and contraception were defeated in one contest after another in the US last month, and opinion polls in the UK suggest that women voters are deserting the Conservatives in droves.

The idea that placing women in positions of authority over men is somehow against the natural order of things sounds quaint in the 21st century. Yet it still strikes a chord with a surprising number of women – not just in the church but also, shamefully, in politics. On Monday there wasn't a single woman on the government frontbench to hear George Osborne announce the next governor of the Bank of England. Women ministers don't need to bother their little heads about finance, it appears, any more than women in the church need to put on robes and tell male priests what to do in their own parishes. After last week it also seems that women don't need, or don't have the opportunity, to apply for the job of director general of the BBC.

This goes some way to explaining the power politics behind otherwise inexplicable decisions. Faced with a gap between the rhetoric of equality and what actually happens within organisations, it's not so surprising that some women choose the safe option of identifying with traditional centres of power. Look at those "first ladies" who find it easier to get close to power than seek it on their own behalf. When Carla Bruni-Sarkozy announces in Vogue that women don't need feminism, she's speaking as a woman who's experienced the material advantages of attaching herself to one of the world's most powerful men.

These women have got where they have – somewhere quite comfortable – without rocking the boat, and they're not keen on women who challenge the status quo. Identifying with men is a traditional means of negotiating patriarchal power, and women who go down that route tend to share reactionary male views of other women. If you're a conservative woman in the Church of England, the prospect of "pushy" women getting power is quite scary, so of course you're going to vote against it. The last thing any traditional woman wants to be accused of is appearing confrontational, even if accepting male power is self-defeating in the long run.

In many ways, women voting against women is hardly a new phenomenon. Before the first world war, the threat of becoming "unsexed" was used against the suffragettes, scaring some women into joining the Anti-Suffrage League founded in 1908 by the novelist Mrs Humphry Ward.

Ward is a cautionary figure in the history of female emancipation, a bestselling novelist who took her campaign to extremes, getting her son Arnold elected as a Conservative MP so that he could campaign against votes for women. Ward had so internalised the notion of power as male that she couldn't see the difference between wanting equality and wanting to be a man. I suspect a similar confusion lies behind the synod's vote, at least on the part of lay members who fear that women would lose their femininity if they became bishops. It's not an unusual fear among women who aspire to some form of political involvement, as we can see from yesterday's news that a WI branch in Devon is holding pole-dancing classes.

In her 1983 book Right-Wing Women, Andrea Dworkin argued that some women acquiesce to male authority in order to gain protection from male violence. She was right, but it isn't just fear of violence that makes women act against their long-term interest. There's also the little question of approval and status, as Vogue's interview with Bruni-Sarkozy reveals. "I'm not at all an active feminist," trills the wife of the former president of France. Channelling her inner housewife evidently works for her, even if it's not a role most modern women aspire to.