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When you think about “gender equality,” the first person who comes to mind probably isn’t LeBron James. That may be changing. James is part of Sheryl Sandberg’s recently launched #LeanInTogether, a campaign that advocates for couples sharing caregiving and breadwinning responsibilities. To help engage men in the conversation, NBA and WNBA players like James are now joining  a chorus of thought leaders in attesting to the merits of 50/50 egalitarianism—benefits that include stronger, more sex-filled marriages; longer, healthier lives; and better-behaved children whose aspirations won’t be limited to sex-stereotyped jobs. Sandberg’s Lean In Foundation has even published tips about how men can help women at and at .

But this campaign may be addressing a problem that doesn’t really exist. According to a study in the latest American Sociological Review, most men already want an egalitarian household, and don’t need to be convinced.

In this experimental survey conducted on a nationally-representative sample of unmarried, childless American men and women, ages of 18 to 32, David Pedulla and Sarah Thébaud how couples would ideally like to divide their work and family responsibilities. The majority of both women and men opted to share breadwinning and caregiving equally with their partners. The sociologist Kathleen Gerson a similar result in 2010, and reports from and the Boston College also say that men’s desire to spend more time with their children is growing. Some men are even willing to take on a full-time parenting load, with wives as sole breadwinners of the family. While still small in absolute numbers, the ranks of stay-at-home fathers doubled from 1 to 2 million in the last decade. Millennial men in particular are less likely than older generations to that the burden of domestic work and childcare will default to the mother.

So what destabilizes couples’ plans for a 50/50 balance? Simply put, two policy gaps: the first between women and men, and the second between policy ideals and policy realities. Pedulla and Thébaud told their experimental group that employers would offer supportive work-family policies to employees—specifically, paid family leave, subsidized childcare, and flexible workplace practices. No such policies were mentioned to the control group. Women in the experimental group—the majority of whom were already inclined to choose a 50/50 sharing arrangement—were significantly more likely to choose an egalitarian relationship. 95 percent of women with some college chose it, and 82 percent of women with high school or less chose it over the more traditional path of primary caregiver, secondary earner. The idealized policies put forth in the study allowed the women to envision how sharing breadwinning and caregiving roles realistically could happen in their lives.

The men, however, were not affected significantly by the existence of work-family policies. More highly educated men did bump up their preference for equally sharing breadwinning and caregiving, while less educated men’s preference fell, but neither difference was statistically significant. The reason the policies had less impact on the men, the authors argue, is that the cultural expectation for them to engage in breadwinning—even avoiding substantial family caregiving to do so—is so strong that it is “impervious to policy context.” They may feel they have more to lose than gain.

That means Sandberg’s #LeanInTogether confronts the challenge of advancing an image of masculinity that . No wonder she recruited the likes of LeBron James.

But it will take more than NBA heavyweights to solve this problem. Most men don’t actually need convincing that “leaning in together” is a good idea, but they do need the right kind of nudge to break old patterns of behavior and crack the shell of their “imperviousness” to policy realities.

One promising step: employer policies that offer specific incentives for men to do more caregiving. Paternity leave is an obvious (and much discussed recently) start, but only of men (globally) get it. Polices like those in Sweden, Norway, and Quebec  that require dads to use the leave time or the family loses it men to become involved more at home. Change.org’s equal parental leave policy of 18 weeks for moms or dads removes the assumption that the woman is the default parent, which they hope will also encourage more men to take time off. Next, figuring out how to remove the stigma of and would help. Finally, another line of thinking says that long hours and overwork norms pervasive in organizations today push parents into choosing sex-stereotyped jobs and family arrangements that are far from equal. Solving that problem would go a long way toward bringing dual-earning parents back to a 50/50 balance.

, scholars and writers call for systemic solutions rather than continuing to ask individuals to do all the changing. Certainly asking men to lean in to a greater share of parenting and other domestic responsibilities is laudable. Men should change more diapers, but everyone should be asking their employers to change too.