In 2016, Hillary Clinton was a former secretary of state and senator running against the politically inexperienced real-estate tycoon Donald Trump. She lost. People would vote for a woman, the thinking went, just not that woman.

In 2024, Kamala Harris was the vice president, a former senator, and a former attorney general also running against Trump, who was by then a convicted felon and sexual abuser. She also lost. People would vote for a woman, once again, just not that woman.

The events of the past eight years might prompt some to wonder: If Clinton wasn’t good enough, and neither was Harris, will a woman ever be good enough to be president? What kind of a woman would it take? According to interviews I conducted with six researchers who study gender and politics, sexism was a small but significant factor that worked against Harris. And it’s going to be a problem for any woman who runs for president. “American voters tend to believe in the abstract that they support the idea of a woman candidate, but when they get the real women in front of them, they find some other reason not to like the candidate,” Karrin Vasby Anderson, a communications professor at Colorado State University, told me. In 2017, she wrote an article about the long odds faced by women running for president. The title? “Every Woman Is the Wrong Woman.”

It’s important not to overstate the role that sexism played in Harris’s loss. She’s the vice president of an unpopular incumbent. Although the U.S. economy writ large is objectively strong, many voters feel pinched by high inflation and interest rates. And after President Joe Biden dropped out of the race in July, Harris had less than four months to make her case to the American public. A very small number of people have ever run for president, and, well, someone has to lose.

[Read: The shadow over Kamala Harris’s campaign]

But some people are biased against female presidential candidates. In 2017, a study found that about 13 percent of Americans were “angry or upset” about the idea of a woman serving as president. In an experiment that same year using hypothetical political candidates, Yoshikuni Ono and Barry Burden, political scientists at the University of Wisconsin at Madison, found that voters punish female candidates running for president by 2.4 percentage points. This means that a hypothetical female candidate would get, say, 47 percent of the vote, rather than 49.4 percent if she were a man. This bias against female presidential candidates, Ono and Burden found, was most pronounced among men and among politically unaffiliated voters—two demographics that Harris struggled with. (Because they don’t feel strongly attached to a party, independents rely on other characteristics of the candidates to make up their mind.)

The obvious counterpoint is that, although they are still underrepresented, women have attained other types of high political offices. We’ve never had a female president, but women make up nearly a third of Congress. Twelve governors are women.

The presidency may be different from other elected positions, though. When researchers ask voters to list the traits that they want in a president, they rate masculine-coded traits, such as strength, as more important than feminine-coded ones, such as compassion. “The prestige and the height of the office contributes to the perception that women are just too big of a risk to take,” Nichole Bauer, a political-communication professor at Louisiana State University, told me.

Masculinity is so important to the presidency that candidates often try to cast their male opponents as feminine: Think of George W. Bush painting John Kerry as effete in 2004, and Marco Rubio’s opponents mocking him for his high-heeled boots in 2016. Female heads of state tend to emerge in countries—including Germany and the United Kingdom—that have parliamentary systems, in which leaders are chosen by political parties, not by voters.

But women who behave in masculine-seeming ways are also penalized for not being traditionally feminine. “For a woman to be seen as presidential, she would have to be hyper-masculine, but the moment she does that, she is condemned by a swath of the population for violating norms of femininity,” Caroline Heldman, a gender-studies professor at Occidental College, told me. “Sarah Palin tried to straddle the masculine-feminine line really wide, ripping the guts out of a moose, and Hillary Clinton barely stepped on either side of the line with her pearls and her pants. It just doesn’t matter. They all get beaten up in the same sexist ways.”

[From the November 2020 issue: Kamala Harris’s ambition trap]

Members of Congress, meanwhile, aren’t held to this same macho standard. There are more of them, they individually have less power, and they are seen as servants of the people. They’re middle managers to the president’s big boss. And although governors are also chief executives, they don’t command an entire nation’s army. Their families aren’t held up as an ideal American family, with the father in charge. As a female presidential candidate, “you’re upsetting not just our idea of what presidents should be,” Anderson said, “but you’re upsetting a whole bunch of gender norms.”

In their study, Ono and Burden found that the hypothetical female candidates weren’t disadvantaged if they were described as running for Congress rather than for president. Burden told me he suspects this is because there has never been a female president, so voters strain to imagine what a female president would be like.

This creates a maddening situation in which a woman can’t get elected president because there’s never been a woman elected president. Several of the researchers I interviewed were nevertheless doubtful that one would win the presidency anytime soon. “It would be really great to see a woman in the White House in my lifetime, but I’m very pessimistic,” Heldman said. Anderson told me that nominating another woman would be a “strategic risk” for either party.

Essentially, a female candidate would have to overcome her femaleness in order to win a presidential race. She would have to be running with significant tailwinds—as a “change” candidate during a terrible economy, say—so that voters wouldn’t pay too much attention to her gender. This is similar to what happened in 2008: An unpopular Republican was president, the economy was a wreck, and the preternaturally charismatic Barack Obama stepped into the breach. He became the first Black president, and now no one questions whether there could be another. But we’re still holding out for the female Obama. We might be waiting for a while.