Jill Filipovic is a journalist based in New York and author of the book " The H-Spot: The Feminist Pursuit of Happiness ." Follow her on Twitter . The opinions expressed in this commentary are solely her own. View more opinion articles on CNN.

(CNN) Can a woman win the presidency? According to an explosive story broken by CNN today, Bernie Sanders didn't think so. He allegedly listened to Warren explain her strengths as a candidate -- she would appeal to a wide swath of voters with her economic policies, and scoop up support from female voters -- only to tell her that a woman couldn't win.

Sanders denies saying any of this. Warren's spokesperson declined to comment for the CNN story, which was sourced via two people familiar with the meeting, and two people Warren spoke with immediately afterwards.

This story also comes as, according to Politico, the Sanders campaign (which offered no comment on the reporting) is ramping up its attacks on Warren, slamming her as an out-of-touch elitist (unlike, apparently, Sanders, who has spent his entire career in politics).

As they did in 2016, the Sanders campaign and Sanders fans have come under criticism for what often seem like disproportionate attacks on even the gentlest of critics. These would include particularly women and people of color on the left who are perceived as purveyors of "identity politics," who believe that sexism, racism and classism intersect and impact our lives, but that class is not the single most important and influential category (and who do not believe that ending classism or crushing capitalism would by definition end sexism and racism).

Sanders has complained in the past about what he seems to see as the rise of identity politics in the Democrat electorate -- the idea that it matters to have women, people of color, and other traditionally marginalized groups in positions of power. "It's not good enough for someone to say, 'I'm a woman! Vote for me!'" Sanders said in 2016.

Of course, no one has ever said that saying "I'm a woman! Vote for me!" is good enough. That characterization is itself demeaning and insulting, and suggests that talking about identity at all is akin to asking for standards to be lowered. In reality, women face very high barriers to entry into traditionally male fields (like politics). Just look at Elizabeth Warren: She nearly had to end her teaching career because she was a mom struggling to find childcare.

She knows, down to her bones, how much potential is wasted because the United States does not meet women's most basic needs -- her own potential was nearly a casualty of bad policy. If we want a government that represents the people, then it needs to be representative. And that means more women in office, breaking a streak of 100% male executive leadership for more than 200 years.

Will it be difficult? Yes -- breaking the glass ceiling always is. But the unknown always seems impossible until it doesn't. Just look at Barack Obama, the first (and still only) African-American president of the United States. We are a nation born of the founding sin of slavery, where Jim Crow was the law; a nation still marked by racism and bigotries both subtle and virulent. Who believed that a black man could be elected president -- and in a landslide no less?

Or a less inspiring example: Who would have believed that a notoriously corrupt and famously tacky New York real estate rich boy turned Twitter-happy, mean-spirited game show host could be elected president of the United States? It seemed like a joke -- an impossibility -- until it wasn't.

By comparison, imagining a woman in the Oval Office doesn't seem all that unbelievable.

If Sanders did in fact tell Warren that a woman couldn't win, he was both sexist and giving voice to what a whole lot of Americans seem to believe: That Hillary Clinton's presidential fate was proof of women's electoral weakness. And there's no doubt that misogyny played a role in Clinton's loss (although it is worth noting here that millions more Americans voted for her than for Donald Trump).

But we don't look at the losses of white men -- and a white man has lost every four years for more than 50 election cycles -- and conclude that white men can't win. We conclude only that a man didn't win.

We know that there are particular barriers to women winning executive offices. But we also know that when women run, they fare just as well as men . They're just less likely to run in the first place. And when they do run for elected office, they do it later in life than men do -- like Elizabeth Warren, who won her first-ever race and secured a Senate seat at age 63, as compared to Bernie Sanders, who first ran for office in 1972, when he was 30 (he ran, and lost, a race for governor of Vermont on a Liberty Union Party ticket).

Sanders should know better than anyone that even significant public bias doesn't make one an electoral lost cause: Nearly half of Americans say they wouldn't vote for a socialist for president, no matter the candidate's qualifications. Of course, what people tell surveyors and what they actually do are not always aligned, and as voters get to know a candidate and learn more about their personality and what they promise to do, decisions change.

But that's almost half of the voting population who have written Sanders off from the get-go. By contrast, 94% of Americans say they would vote for a woman. Sanders, in other words, has the higher hill to climb. I think he can do it. But if he (or anyone else) is worried about which candidates simply cannot overcome Americans' deeply-held biases, well -- Sanders' candidacy poses a lot more to worry about.

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Sanders remains in the race, suggesting that he believes Americans can overcome their preconceptions and vote for someone who is markedly different than most of the people who have previously held the office of the presidency. On that, he is 100% correct.