Millennial dads want to play an equal role in child rearing. Really, they do.

They just aren’t.

The New York Times recently highlighted a study published in the American Sociological Review that found most men and women ages 18 to 32 have egalitarian attitudes about gender roles, across education and income levels. But these ideals come up against a hard reality when men actually have kids, the study found, with many fathers saying they’d be stigmatized for cutting back at work.

“I can safely can say that fathers’ aspirations to be more involved in caregiving have increased in recent years, but their actions are not quite aligned with their aspirations yet,” said Brad Harrington, executive director of the Boston College Center for Work & Family.

The most recent study from Families and Work Institute, a national organization, highlighted the convergence of work-life ideals for men and women. Only 35 percent of employed millennial men without kids said they thought men should be the breadwinners while women should “take care of the home and children.”

But once men actually have kids, the study found their attitudes shift, with 53 percent of millennial men with children saying it was best for men and women to take traditional roles. Why the change in opinion?

“One reaction is, ‘Yeah, it figures. Men talk a good game,’” Harrington said. But there is evidence that something more complicated is going on.

Some studies suggest men feel they will be stigmatized at work if they take parental leave or cut back on hours after having children. The Boston College Center for Work & Family studied the changing role of fathers for six years, and found that working fathers may experience as much or more work-family conflict than their female counterparts.

The organization’s 2011 research showed 16 percent of men took no time off following the birth of a child, while 96 percent took two weeks or less. Gender stereotypes and the short duration of men’s parental leave patterns caused 99 percent of working fathers to say they felt their supervisor expected “no change to occur to their working patterns as the result of their becoming parents.”

Massachusetts expanded their parental leave law in April, requiring smaller businesses to grant fathers eight weeks of unpaid leave. But in a parental leave study Harrington conducted last year, most fathers surveyed said they expected paternity leave to be paid. The Boston Globe reports that more than half of U.S. employers provide some form of paid maternity leave beyond vacation or sick time, but only 14 percent offer paid paternity benefits, according to the Families and Work Institute.

If paid paternity leave was offered, Harrington said, the most common response was that fathers would take the leave offered to them, whether it was two, four, or six weeks.

But most fathers said they wouldn’t reduce their hours once paternity leave was over.

“Some feared if they took more time, they’d have a pile of work once they returned or that someone would take their job while they were gone,” Harrington added.

Still, millennial fathers are making strides toward spending more time at home. The Families and Work Institute study also found that millennial fathers spend an average of 4.1 hours per workday with their children, compared to the 2.4 hours dads in 1977 spent. Mothers under 29 spend an average of 5.4 hours per workday with their kids.

“Men are being more outspoken about their role as fathers and more assertive about their role in the home,” Harrington said. “But is it common they will reduce hours? No, that’s still very uncommon.”

Justine Hofherr can be reached at justine.hofherr@globe.com. Follow her@Jhofherr29

Millennial Dads Want To Share The Caregiving Load. So Why Aren’t They?