Hillary Clinton and Bernie Sanders have had their first real campaign trail brawl, and it's about sexism.

It all started when Clinton turned a moment from the Democratic debate, one in which Sanders rebuked her position on gun control as "shouting," into a feminist rallying cry.

"I've been told to stop, and, I quote, 'shouting about gun violence,'" Clinton said at the Democratic National Committee Women's Leadership Forum. "Well, first of all, I'm not shouting. It's just when women talk, some people think we're shouting."

The line was an instant hit with women who know how it feels to be judged for their tone instead of what they have to say, and who are tired of the double standard that encourages men to be aggressive but punishes women for it.

The line was not a hit with the Sanders campaign. His staffers balked at the suggestion that their candidate might have said something sexist, and they fought back — using condescending language about how Clinton would make a "great vice president," which sparked a whole new round of questions about sexism.

A lot of people have tried to judge whether Sanders or his staff actually said something sexist, or whether it was unfair of Clinton to bring up the issue in the first place.

These questions don't help us understand what's really going on here — and what's going on with gender politics in America lately. It's not about placing blame or judging motives. There's decent evidence that Sanders really didn't intend any sort of gender discrimination or sexism with his remarks. As he has pointed out, Sanders has scolded opponents for uselessly "shouting" about guns many times before. He even chided Martin O'Malley about "raising our voices" during the same exchange, although he was less forceful about it with O'Malley than Clinton.

The flap between Clinton and Sanders is about something different from the outright sexism that Sanders swears he didn't intend. What Clinton was pointing out was a subtler, more pervasive kind of discrimination — and the disbelieving response of both the Sanders campaign and the media shows why she was right to bring it up.

Clinton made a spot-on point about how women are perceived

Clinton didn't say or imply that Bernie intentionally slighted her based on her gender. She did imply that her gender made him see her differently, and that many women have this same experience all the time. That idea should be a lot less controversial than it often turns out to be.

There's a reason so many women instantly identified with her remark. It's because across the board, people tend to mentally turn up the volume when women speak — and research proves it. Even though women are interrupted more often and talk less than men, people still think women talk more. People get annoyed by verbal tics like "vocal fry" and "upspeak" when women use them, but often don't even notice it when men do. The same mental amplification process makes people see an assertive woman as "aggressive," which gets in the way of women's personal and professional advancement. Women are much more likely to be perceived as "abrasive" and get negative performance reviews as a result — which puts them in a double bind when they try to "lean in" and assertively negotiate salaries.

These kinds of implicit biases are sexist, but having them doesn't make someone "a sexist" — or if it does, it makes all of us sexists. It doesn't matter how smart you are or whether you are a man or a woman; everyone has some implicit biases against women.

That means it's practically meaningless to "accuse" someone like Sanders of sexism in this case, or for Sanders to "defend" himself against such charges. We often understand the term "sexist" to mean "someone who actively hates and degrades women in a way that a decent person would not do." Of course, plenty of people fit this description, but that's not what this debate is about.

It's about paying more attention to the ways that everyone perceives women differently — and hopefully changing those perceptions, since there's evidence that being aware of our own biases can help us overcome them.

Sanders's staff perfectly illustrated why it's so hard to have a sane discussion about gender bias

The Sanders campaign started preparing for battle at the suggestion that Clinton might be accusing their candidate of sexism.

"If they’re going to have a campaign that attacks Bernie on gun safety and implies he engages in sexism, that’s unacceptable," chief strategist Tad Devine told Politico. "If they’re going to engage in this kind of attack, they need to understand we’re not going to stand there and take it." Devine also told Bloomberg that Clinton's remark basically forced Sanders to "fire a shot across their bow."

In that same Bloomberg interview, Sanders's campaign manager, Jeff Weaver, made some remarks about Clinton that came off as incredibly patronizing. "Look, she'd make a great vice president," Weaver said, later adding, "We'll even interview her."

Reporter John Heilemann said Weaver was "at least half-joking" when he said that, but a lot of people didn't find it funny. The comment reeked of head-patting condescension, the kind that highly qualified women often endure from men who don't take them seriously. Weaver insisted that his comments were "edgy or snarky but nothing more," and also doubled down on the idea that Clinton had launched a "vicious attack" on the Sanders campaign with her "accusations of sexism."

The media also went nuts over "accusations of sexism" and overamplified women's concerns about it until they sounded like "shouting" (literally, in the case of one Politico headline). When Emily's List president Stephanie Schriock criticized Weaver's remarks on Twitter as a "condescending insult by a team who knows better," a New York Times headline blew up her tweet into, "Emily's List Official Accuses Bernie Sanders Team of Sexism." At Slate, William Saletan said that Clinton was "smearing" Sanders as "a sexist" and "manipulating women and abusing feminist anger for her own advantage."

This flare-up is an example of the kind of thing that keeps happening whenever women try to point out microaggressions — all the little daily sexist slights that may not mean much individually but add up over a lifetime. Even well-meaning progressives sometimes freak out over discussions of "sexism," because they think they are being personally accused of being sexist. This makes people defensive, and it leads to the kind of bunker mentality that makes Weaver call Clinton's winking quip a "vicious attack."

We need to keep talking about gender bias on the campaign trail, but it doesn't need to be this difficult

Gender bias is a real and present obstacle for women every day, but it's not always obvious. That's why more feminists and social justice activists are speaking out about microaggressions — not to shame and belittle people, but to draw people's attention to their own blind spots, which everyone has, and ask them to notice and work on fixing them.

Hillary Clinton is playing up her gender and her feminism as a strategy, but it's probably not just a ploy to energize her base. Clinton may feel she has no choice but to actively confront these everyday-background-noise forms of sexism — the kinds that, over time, have made it harder for people to associate women with leadership and positions of power (like the presidency).

And Sanders, who considers himself a feminist and is proud of his record on women's rights, owes it to himself to take Clinton's callouts seriously. Like anyone else, Sanders needs to be aware of the disproportionate impact that seemingly neutral statements can sometimes have on women — that, for instance, people can respond very differently to the idea of women "shouting" than men.

Sanders actually seems to respond well to callouts. After being interrupted by Black Lives Matter protesters, he started talking much more often and with much deeper understanding about racial injustice. It ended up being a learning experience that Sanders and his campaign turned to his advantage.

There's already evidence that Sanders may have learned the lesson he needed to from this incident. He was smart about the damage control over Weaver's comment, and said flat out that the VP remark was "inappropriate." But just as with Black Lives Matter, Sanders will quickly find that it's not enough for feminists to hear endless recitations of how great his voting record is on women's rights. He will have to demonstrate that he's really working to understand what women go through on a daily basis.