I know Hillary Clinton mostly in the way we all do, as a public figure in good times and bad, one who became part of our lives and even our dreams. I once introduced her to a thousand women in a hotel ballroom. Standing behind her as she spoke, I could see the binder on the lectern with her speech carefully laid out – and also that she wasn’t reading from it. Instead, she was responding to people who had spoken before her, addressing activists and leaders she saw in the audience, and putting their work in a national and global context – all in such clear and graceful sentences that no one would have guessed she hadn’t written them in advance. It was an on-the-spot tour de force, perhaps the best I’ve ever heard.

But what clinched it for me was listening to her speak after a performance of Eve Ensler’s play Necessary Targets, based on interviews with women in one of the camps set up to treat women who had endured unspeakable suffering, humiliation, and torture in the ethnic wars within the former Yugoslavia. To speak to an audience that had just heard these heartbreaking horrors seemed impossible for anyone, and Hillary had the added burden of representing the Clinton administration, which had been criticised for slowness in stopping this genocide. Nonetheless, she rose in the silence, with no possibility of preparing, and began to speak quietly – about suffering, about the importance of serving as witnesses to suffering. Most crucial of all, she admitted this country’s slowness in intervening. By the time she sat down, she had brought the audience together and given us all a shared meeting place: the simple truth.

When she left the White House and decided to run for the US Senate from her new home in New York State – something no first lady, not even Eleanor Roosevelt, had dared to do – I was blindsided by the hostility toward her from some women. They called her cold, calculating, ambitious, and even “unfeminist” for using political experience gained as a wife. These were not the rightwing extremists who had accused the Clintons of everything from perpetrating real estate scams in Arkansas to murdering a White House aide with whom Hillary supposedly had an affair. On the contrary, they mostly agreed with her on the issues, yet some were so opposed to her that they came to be called Hillary Haters. It took me weeks of listening on the road to begin to understand why.

In living rooms from Dallas to Chicago, I noticed that the Hillary Haters often turned out to be the women most like her: white, well educated, and married to or linked with powerful men. They were by no means all such women, but their numbers were still surprising. Also, they hadn’t objected to sons, brothers, and sons-in-law using family connections and political names to further careers – say, the Bushes or the Rockefellers or the Kennedys – yet they objected to Hillary doing the same. The more they talked, the more it was clear that their own husbands hadn’t shared power with them.

If Hillary had a husband who regarded her as an equal – who had always said this country got “two presidents for the price of one” – it only dramatised their own lack of power and respect. After one long night and a lot of wine, one woman told me that Hillary’s marriage made her aware of just how unequal hers was.

‘Two presidents for the price of one’ ... the Clintons. Photograph: Luke Frazza/AFP/Getty Images)

Haters condemn her for staying with her husband despite his well-publicised affairs. It turned out that many of them had suffered a faithless husband, too, but lacked the ability or the will to leave. They wanted Hillary to punish a powerful man in public on their behalf. I reminded them that presidents from Roosevelt to Kennedy had had affairs, but the haters identified with those first ladies and assumed they couldn’t leave. It was Hillary’s very strength and independence that made them blame her. When I tried describing the public condemnation Hillary would have suffered had she abandoned her duties in the White House for such a personal reason, this changed the minds of some – but not many.

Finally, I resorted to explaining my own reasons for thinking the Clintons just might be, in Shakespeare’s phrase, “the marriage of true minds”. Yet when I brought this up, some Hillary Haters became even angrier. The fact that Bill valued Hillary as an equal partner – and vice versa – seemed to make them more aware that their own marriages were different. It dawned on me that if a sexual connection is the only bond between a husband and wife, an affair can make her feel replaceable – and perhaps cause her to be replaced. This was not only emotionally painful but devastating when it also meant losing social identity and economic security as well. I began to understand that Hillary represented the very public, in-your-face opposite of the precarious and unequal lives that some women were living. In a classic sense, they were trying to kill the messenger.

Their projections made me realise that I was projecting, too. I couldn’t understand why Hillary wanted to go back to Washington, and so campaigned for the Senate in the first place. Why ask for six more years with a target painted on her back? It seemed quixotic and self-punishing, especially now that she had such great alternatives as creating her own foundation, and supporting female empowerment globally.

Finally, I had to admit that the latter would have been my choice, not hers. If she was willing to face a degree of combat that I couldn’t even imagine, I should celebrate.

As my own part of her senate campaign, I began to invite Hillary Haters to the living room events where Hillary herself was fundraising. To my surprise, all but a few turned around once they had spent time in her presence. This woman they had imagined as smart, cold, and calculating turned out to be smart, warm, and responsive. Instead of someone who excused a husband’s behaviour, she was potentially, as one said, “a great girlfriend” who had their backs.

They also saw her expertise. For instance, George Soros, the Hungarian-born financier and philanthropist, introduced her in his Manhattan living room by saying, “Hillary knows more about eastern Europe than any other American.”

After she was elected to the US Senate on her own merits, she worked constructively, even with old enemies there, and was solidly re-elected to a second term. I began to hear the first serious talk of Hillary Clinton as a presidential candidate. By the time the election of 2008 was in the wind, she had a higher popularity rating than any other potential candidate, Republican or Democrat.

Steinem with Hillary Clinton at a Girls Learn International event in 2006. Photograph: Jemal Countess/WireImage for Glamour Magazine

Whenever I was on the road before the primaries, I saw a revival of this unconscious coalition in audiences that were interested in politics as never before. There was enthusiasm for these two new faces that stood for a shared worldview. In audiences from very blue states to very red ones, support was more like a Rorschach test than a division by race and sex. For instance, 94% of black Democrats had a favourable view of Hillary Clinton, compared to an 88% favourable view of Obama. After all, he was new on the national stage and the Clintons had earned a reputation for racial inclusiveness that caused African American novelist Toni Morrison to famously call Bill Clinton “the first black president”. Both white and black women were more likely than their male counterparts to support Hillary Clinton – and in my observation, also more likely to believe that she couldn’t win. Male and female black voters were more likely than white voters to support Obama and also to believe he couldn’t win. Each group was made pessimistic by the depth of the bias they had experienced.

Some mostly white audiences seemed to hope this country could expiate past sins by electing Obama. As one white music teacher rose in an audience to say, “Racism puts me in prison, too – a prison of guilt.” Many parents of little girls, black and white, were taking them to Clinton rallies so they would know that they, too, could be president. Older women especially saw Hillary Clinton as their last and best chance to see a woman in the White House. And not just any woman, as one said: “This isn’t just about biology. We don’t want a Margaret Thatcher, who cut off milk for schoolchildren.”

They wanted Hillary Clinton because she supported the majority interests of women. On the other hand, many young, black, single mothers said they supported Obama because their sons needed a positive black male role model.

But the press, instead of reporting on these shared and often boundary-crossing views as an asset for the Democratic party – after all, Democratic voters would have to unify around one of these candidates eventually – responded with disappointment and even condescension. They seemed to want newsworthy division. Soon frustrated reporters were creating conflict by turning any millimetre of difference between Hillary Clinton and Obama into a mile. Since there was almost none in content, they emphasised ones of form. Clinton was entirely summed up by sex, and Obama was entirely summed up by race. Journalists sounded like sports fans who arrived for a football game and were outraged to find all the players on the same team.

It dawned on me that in the abolitionist and suffragist past, a universal suffragist movement of black men and white and black women also had been consciously divided by giving the vote to black men only – and then limiting even that with violence, impossible literacy tests, and poll taxes. Now, this echo of divide-and-conquer in the past was polarising the constituencies of two barrier-breaking “firsts”, never mind that the candidates were almost identical in content. As in history, a potentially powerful majority was being divided by an entrenched powerful few.

There was enthusiasm for these two new faces who stood for a shared worldview ... senators Obama and Clinton in 2008. Photograph: © Jim Young/Reuters/Corbis

Maybe attributing a divide-and-conquer motive was unfair in a country that treats everything like a horse race, but there had to be some reason why the press did not consider what I witnessed on the road – delight in two “firsts” with similar purpose – worth reporting.

Soon, a person or a group’s choice of one candidate was assumed to be a condemnation of the other. I could feel fissures opening up between people who had been allies on issues for years. The long knives of reporters, plus a few shortsighted partisans in both campaigns, deepened those fissures until they bled.

As the New York primary approached, I certainly wasn’t against either candidate, but I still had to decide who to vote for. So I sat down with a yellow pad and made a list of pros and cons for each.

The only obvious difference was experience. This primary race was a rare case in which the female candidate was more experienced in big-time political conflict than the male candidate. She was more familiar with extremists for whom there was no middle ground. I knew that outside the women’s movement, I would be better liked if I chose Obama. Women are always better liked if we sacrifice ourselves for something bigger – and something bigger always means including men, even though something bigger for men doesn’t usually mean including women. In choosing Hillary, I would be seen as selfish for supporting a woman “like” me. But that was a warning, too. Needing approval is a female cultural disease, and often a sign of doing the wrong thing. There was one more note on my yellow pad. Because I still believed it was too soon for Hillary or any woman to be accepted as commander-in-chief, I wrote: If I were Obama, I would not feel personally betrayed by lack of support from someone like me, a new ally. If I were Hillary Clinton, I might feel betrayed by a longtime supporter who left me for a new face. In other words: Obama didn’t need me to win. Hillary Clinton might need me to lose.

Once again the road educated me – by showing me what voters were subjected to. I began to think that the wait for a female president might be even longer than I imagined. On campuses, I saw young men wearing T-shirts that said “Too bad OJ didn’t marry Hillary” (all caps). I watched as MSNBC political analyst Tucker Carlson said of Hillary Clinton: “I have often said when she comes on television, I involuntarily cross my legs.”

Obama awards the presidential medal of freedom to Gloria Steinem in 2013. Photograph: Bill O’Leary/Washington Post via Getty Images

A woman reporter for the Washington Post wrote about a Hillary suit jacket that disclosed a bit of cleavage and called it “a provocation”. No such charge had been levelled at male presidential candidates, from John F Kennedy to Obama, when they were photographed on the beach in bathing suits. About Hillary, Rush Limbaugh asked: “Will this country want to actually watch a woman get older on a daily basis?”

No wonder such misogyny was almost never named by the media. It was the media.

In making my list about the pluses and minuses of Hillary Clinton and Barack Obama, I discovered I was angry. I was angry because it was OK for two generations of Bush sons to inherit power from a political patriarchy, but not OK for one Clinton wife to claim experience and inherit power from a husband whose full political partner she had been for 20 years. I was angry because young men in politics were treated like rising stars, but young women were treated like – well, young women. I was angry about all the women candidates who put their political skills on hold to raise children – and all the male candidates who didn’t. I was angry about the human talent that was lost just because it was born into a female body, and the mediocrity that was rewarded because it was born into a male one. And I was angry because the media took racism seriously – or pretended to – but with sexism, they rarely bothered even to pretend. Resentment of women still seemed safe, whether it took the form of demonising black, single mothers or making routine jokes about powerful women being ball-busters.

Once Obama won, a few wise people in his and Hillary’s campaigns – who had been in touch all along – knew there had to be a healing. With my friend and colleague Judy Gold, who was in charge of women’s issues for Obama’s campaign, I planned what we knew would be the first of many healing meetings. There were heartbroken older women who now knew they would never live to see a woman in the White House. There were younger ones who had grown up being told they could be anything, then been shocked by Hillary’s treatment and defeat. African American women and men who had supported Hillary also worried that some would punish them for working across racial lines. Oprah Winfrey and other women in public life who had supported Obama paid a price, too. Some criticised them for not supporting Hillary Clinton, since women were their main supporters and constituency. This was also true for Karen Mulhauser, a white woman and an important and longtime feminist leader, who supported Obama. I had written and spoken in support of their right to choose Obama, and now they, too, helped to heal the wounds of Hillary Clinton’s defeat.

As my last campaign effort, I made hundreds of buttons that said: HILLARY SUPPORTS OBAMA SO DO I. Then I got on the plane to Washington, went to join the crowd at her historic and generous concession speech – in which she pledged her wholehearted support to Obama – and distributed the buttons to the audience. They were in great demand.

This is an edited extract from My Life On The Road, by Gloria Steinem, published by Oneworld, at £14.95. To buy it for £10.47, go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.