Wednesday night’s New Hampshire town hall on CNN found both remaining Democratic candidates in relatively subdued form. Bernie Sanders talked about his folk music album, his tiny red Chevrolet, his 27-year marriage to his wife Jane. Hillary Clinton reflected on her granddaughter, life on the campaign trail, and the exhaustion of fame. But the relatively sedate atmosphere of the event was compromised by questions to each candidate about their ongoing battle over who is the true “progressive” in the race.

The flare-up began earlier this week when Sanders told MSNBC that on “some days” Clinton is a progressive, while on others she identifies as a “moderate.” On Wednesday, the official Twitter account associated with Clinton’s campaign took offense to Sanders’s remark. But the Sanders campaign Twitter account was ready with its own series of tweets impugning the former secretary of state’s record on progressive issues, which it shortly rolled out. Clinton’s campaign hit back, and Twitter users descended into a fevered discussion of what exactly constitutes progressivism.

The beef was long in the making, and a Twitter spat is rarely flattering to any of the parties involved. But this one has helped both candidates by illuminating the core difference between their campaign’s respective messages—a difference that may dominate the campaign going forward, and even decide who wins the Democratic primary. 

On Wednesday night, CNN’s Anderson Cooper presented Clinton with a shortened form of the issue at hand, asking her point-blank if she’s a progressive.

You asked me this question in the first debate,” Clinton observed, “and I said I’m a progressive who likes to get things done. And I was somewhat amused today that Senator Sanders has set himself up as the gatekeeper of who gets to be a progressive... Under the definitions flying around on Twitter, President Obama would not be a progressive, Vice President Joe Biden would not be a progressive... I’m not going to let that bother me. I know what I stand for, I know what I’ve done.”

When given an opportunity to address the Twitter battle himself, Sanders merely reiterated that “you can’t go and say you’re a moderate on one day and be a progressive on the other day … you can’t be a moderate and a progressive. They are different.”

Later, when Cooper asked Clinton what’s not to like about the idea of a “political revolution,” Sanders’s much-favored slogan, Clinton replied, “That’s for Senator Sanders to explain, since that certainly is the core of his message to young people. I have a different take on it. I think the progress we have made, particularly the Democratic Party has made, has been hard fought for and hard won, and I want to defend it.” 

In her responses to Cooper on the Twitter kerfuffle, Clinton honed in on the real stakes of the progressive question. It’s not just about establishing one’s place in any kind of leftward movement, but rather about staking one’s appeal to votersparticularly young voters—who are suspicious of pragmatic compromises that might pull policies rightward, or merely maintain the status quo. The term itself is at stake, and the population most interested in the outcome seems to be young people who are deeply invested in progress, and who do not want the politics of their parents.

Young voters likely find the majority of their memory dominated by the Great Recession, and their concerns marked by its privations: student debt, high healthcare costs, and limited job prospects. Millennials find ourselves faced with plenty of education and little to show for it; lower rates of home ownership than our parents, higher rents, and the sense that, despite the gains of the Affordable Care Act, getting sick can still be disastrous for one’s finances. Thus it is no surprise that Sanders dominated the youth vote in the Iowa caucuses, claiming 84 percent of voters between the ages of 17 and 29. With policies like single-payer universal healthcare, a $15-per-hour minimum wage, and universal free college on offer, it would have been somewhat startling if Sanders hadn’t captured the attention of young voters.

But Sanders’s easy way with the young hasn’t pleased Clinton’s supporters, who see in the youth rejection of Hillary both a ridiculous starry-eyed utopianism and a frustrating redefinition of what it means to be progressive. “Bernie’s attractiveness as a candidate relies on the premise of purity—a political value as ancient as politics itself,” Alexandra Schwartz, herself a millennial, recently wrote in The New Yorker. But, Schwartz warned her fellow youths, “purity, a highly useful principle to make use of while running for office, is all but useless to politicians who actually arrive there, and the voters least likely to see that are young ones.” Bernie’s hardline adherence to his principles, in other words, was made to seem a campaign sham. Meanwhile, Schwartz surmised that the “suspicion that political compromise is inherently venal is at the root of the grievances that so many of Bernie’s young supporters harbor against Hillary, whose long record bears the kind of battle scars that are easily dodged by an independent senator from Vermont.” Clinton has the grit, and Sanders the glamour. Clinton’s impurity—her periodic deviation from what young voters now view as proper progressivism—is a symptom of her maturity, and millennials’ disdain for it is a marker of their naïveté. 

So the battle for the true-progressive mantle would seem to be a losing one for each candidate, with Sanders standing accused of manipulating the dreams of children, and Clinton charged with a career-long habit of rank centrism, no better for the recession-disaffected millennial than an emperor without clothes. 

And yet, the situation seems rather opposite. Sanders and Clinton are ready to wage this battle in public precisely because it offers each of them an opportunity to work their best lines, which is why Schwartz’s New Yorker essay likely reinforced more millennial admiration for Sanders than it dislodged. (If I were on Sanders’s campaign team, I would certainly welcome a New Yorker article charging that Bernie is just too damn principled and youthy, along with any number of National Review pieces declaring him just too far left. Bring them on!) Sanders relishes opportunities to remind his voters that he is a man of integrity: At Wednesday’s town hall, his wife, Jane, chose that word as most descriptive of her husband. Likewise, Clinton never misses a chance to revisit her many years of political experience, nor her record of working with Republicans to muscle policies through legislature. “I am a progressive who gets results—and I will be a progressive president who gets results,” Clinton said on Wednesday, adding at another point that, though young voters might not be for her, she will be for them. 

Sanders, meanwhile, didn’t have to make the progressive pitch, or stake his claim to young voters. All he had to do was stay on brand and continue to back his chosen policies, and the same work was done. As the campaign wears on, so too will the fight to claim progressivism—not because it’s particularly illuminating or insightful, but because it’s such a propitious public scuffle for the two campaigns to have.