On Thursday we learned, via Politico, that had Joe Biden run for president, he would have asked Elizabeth Warren to be his running mate. According to reporters Glenn Thrush and Annie Karni, Biden has “recently told associates that Warren would be an equally smart pick for Hillary Clinton.” The Huffington Post reported that several people in the Clinton campaign are also pushing for Warren.

They are right. Choosing Warren would be an uncharacteristically bold and thrilling move for the cautious Clinton, one that would help unite Sanders supporters behind her candidacy while throwing its feminist promise into high relief. Clinton is already playing the woman card; now, to belabor a metaphor, she should double down.

One of the many dispiriting things about this primary season is the degree to which Clinton’s baggage has dampened excitement over the prospect of our first female president. She’s been near the center of power for so long that her possible presidency seems less like a breakthrough than a wearying inevitability. Further, in order to get close to power, she’s consistently subsumed idealism to realpolitik; her career is littered with grim compromises, from reluctantly backing welfare reform to voting to authorize war in Iraq. Thus some progressive women who enthusiastically support Clinton feel like they have to apologize for it. Other progressive women who’d like to vote for a female president feel like they can’t enthusiastically support Clinton. Obama’s campaign created an incandescent sense that America was on the cusp of history. That magic is missing from Clinton’s long slog.

If you haven’t said it yourself, you’ve surely heard it: “Of course I want to see a woman in the White House, but …” Warren on the ticket would annihilate many of those “buts.” She would help to neutralize some of Clinton’s very real flaws; it would be harder to accuse Clinton of doing the bidding of big banks while running with Warren, the scourge of Wall Street. Warren’s presence would give disappointed supporters of Bernie Sanders a reason to rally to the Democratic banner. And by Clinton’s side, she would make it blazingly clear what an epochal moment this is for American women. She’s a choice who could electrify both Clinton’s fiercest progressive critics and her most devoted acolytes.

Of course, an all-woman ticket carries real risk—that’s the flip side of its audacity. Already, Clinton is likely to face misogynist headwinds, and Warren would make them stronger. People sometimes claim that the deep, widespread antipathy to Clinton, particularly among men, is unique to her and has little to do with her gender. Warren’s political career shows us that this is not the case. When she ran for Senate in Massachusetts four years ago, she was regularly disparaged as both a liar and a crone; the Boston Herald referred to her as “Granny.” We were constantly reminded that while people admired her competence, they weren’t sure they liked her. (One poll found that even Democrats found her opponent, Scott Brown, more likeable.) Warren won thanks to a large gender gap: According to a CNN exit poll, Brown won 53 percent of the male vote, but Warren carried 59 percent of the female vote, and women were the majority of the electorate.

It’s possible, then, that Warren could exacerbate rather than ameliorate some people’s—particularly some men’s—resistance to Clinton. As T.A. Frank points out in Vanity Fair, social science research shows that when minorities team up to form a duo, they are judged in more stereotypical terms than they are individually. “If this is a reliable dynamic, then it means that Clinton is seen by voters first and foremost as a Democratic presidential candidate, and not simply a female,” Frank writes. “But if she were to pick Warren as a running mate, gender could start to color many people’s views much more.”

Yet Donald Trump has already ensured that this race is going to be a battle of the sexes, one pitting a feminist woman against an ur-misogynist. Trump rose to his present astonishing political perch by exploiting seething American anxieties about a black president and a demographically changing country. It’s long been obvious that, faced with Clinton, he would start exploiting another set of anxieties about rapidly changing gender roles. He has already started; at a recent rally, he said, “I mean all of the men, we’re petrified to speak to women anymore. We may raise our voice. You know what, the women get it better than we do, folks.”

Whomever Clinton chooses, this is but a faint preview of what the next six months are going to look like. She is not going to win this race by persuading white men who are uncomfortable with women in power. She will do it by turning out the Obama coalition, probably adding more married white women to it. Warren can help her do that. She’s shown that she’s eager to, leaping into the Twitter fray against Trump. If a vice presidential candidate’s job is to attack, Warren is ready. Watching her go after the short-fingered orange chauvinist from now until November will be a pleasure. The fight for the first female president should be a joyful feminist crusade, one that progressives can join without reservation. Warren can make it one.

Read more Slate coverage of the 2016 campaign.