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Female readers, did you gravitate toward certain articles about a recent Pew Report (Raising Kids and Running a Household: How Working Parents Share the Load)? Maybe you clicked on a headline like Equal division of labor at home for working parents? Not exactly (CNN), or “Who does more at home when both parents work? Depends on which one you ask” (Pew Fact Tank), or lingered knowingly over the paragraphs in the many articles that described how mothers do more: more to manage children’s schedules and activities, more chores, more coping with sick days. Much of the reporting included a wry poke at the “fun” statistic: More fathers than mothers say they share equally in the work.

Oh, those dads. They just don’t get it!

Every headline of that sort is something of a punch in the gut to Josh Levs, a well-known CNN journalist who made headlines himself by suing the parent company of his employer over their failure to offer him parenting leave equal to that provided for women, and for men who had babies through adoption or surrogacy. (After he filed his lawsuit, Time Warner changed its policies.) His book about the experience, “All In: How Our Work-First Culture Fails Dads, Families, and Businesses — And How We Can Fix It Together,” makes a powerful case for why parents of all kinds need more support from society, culture and policy — and against wasting too much collective time on the “who does more” trope. When we do, he says, we inadvertently add to the forces that support the status quo while accepting a distraction from the real problem.

“All the numbers show that men and women are putting in equal time for our families,” says Mr. Levs, even if we don’t yet spend that time in equal ways. “We’ve achieved a level of egalitarianism that no one understands.” Research, including the America Time Use Survey, supports the equal overall time premise. Fathers employed full time, on average, spend a little less than an hour more at work daily than mothers in full-time work, while mothers employed full time spend about 1.4 hours a day engaged in managing schedules, driving children to activities, providing physical care and helping with homework compared with about one hour a day for a father working full time. Full-time working mothers spend 1.7 hours a day engaged in housework compared with the 1.2 hours full-time working fathers report spending. Add it up, and mothers spend just under an hour more on the home front — about the same amount of time dads are putting in at work.

When we make the difference in the headline, it’s too easy to forget that, as Mr. Levs says, where we put in the extra time is “not entirely a matter of choice.”

It’s barely necessary to note the long history of societal and cultural forces that put their fingers on the scale of equal distribution of work in and outside the home. Women have long been taught that we’re the caregivers; even without doubting our male partner’s ability to do the same, we can too easily see ourselves as failures if we’re not doing everything for our children ourselves. Men are raised to be breadwinners and to relish the role; even in the least physical of jobs, like law or programming, management manages to create a culture of machismo around pushing the limits of time and sleep. Ironically, fathers seem even more likely to fall into the urge to meet that challenge: Men with a college degree living with their children are more likely to work more than 50 hours a week than men who are childless.

When we trumpet the differences in the ways full-time working men and full-time working women spend their time, are we perpetuating the differences? Mr. Levs thinks so. “People have these stereotypes in their mind,” he says, and they make decisions based on those stereotypes and the network of laws and policies and stigma that has grown up around them. “Why would you want to change your policy to make sure that a man is able to stay at home if all he’s going to do is sit around?”

“Men do less at home” is the old story. The new story is men who place a high value on their time with family and are willing to say so. These are men who recognize that being a part of their children’s lives means driving and scheduling, dealing with the dead gerbil and sitting next to the child creating a poster for the history fair and holding the glue stick along with all the things you end up doing, as a parent, when you’re able to be at home to do them. “Women do more” is the supposedly positive spin on an old story that holds women back as well. It’s “mothers don’t care enough to put in the time at work” in a different guise.

Instead of going for the click and chuckle, we need to headline the numbers that show that fathers and mothers prioritize the same things, and that we all struggle to find a good balance. Those numbers were there, in the most recent Pew report, loud and clear. Among couples with two full-time working parents, most (62 percent) report that mom and dad are equally focused on their careers. Full-time working mothers and fathers alike say that balancing work and family responsibilities is difficult: 57 percent say it’s hard to strike a balance, and 46 percent, including half of full-time working dads, say they don’t spend enough time with their children. Both men and women want a work life that supports their family life, and that desire isn’t new. As Pew noted in a recent blog post: “in a 2013 survey, 41 percent of parents with children under 18 (including somewhat similar shares of mothers and fathers) said it was extremely important for them to have a job that allows them to take time off for child care and family issues.”

“We’re seeing a real convergence of roles in terms of what mothers and fathers are doing, and how they’re spending their time,” said Kim Parker, director of social trends research at Pew Research Center. “We’re not quite at parity, but we’re getting a lot closer.”

“Not quite at parity” doesn’t make a very good headline. But it does make a good case for the need for parity in our approach to family policy. When those “networks of laws and policies and stigma” that Mr. Levs describes instead become a culture that treats fathers and mothers equally with regard to expectations, both at home and at work, then it will be time to worry about who empties the dishwasher more often. Of course, we’ll also need to consider who last took out the trash.