Firms are catching on to paternity leave. Dads? Not so much.

Yahoo Inc. announced in April that new fathers can take eight weeks off at full pay. Bank of America Corp. offers 12 weeks of paid leave, and Ernst & Young a few years ago bumped its leave policy from two weeks to six. Fifteen percent of U.S. firms provide some paid leave for new fathers, according to a survey from the Society for Human Resource Management to be released on Father's Day.

It sounds like progress, but in reality men are reluctant to take time off for a variety of reasons, ranging from a fear of losing status at work to lingering stereotypes about a father's role in the family.

Leave is the norm for women, but men have only become a part of the discussion as traditional housewife and breadwinner roles have shifted. Countries around the world, such as Sweden and Portugal, have mandated leave for fathers, but leave in the U.S. remains stubbornly short—if it is taken at all.

Approximately 85% of new fathers take some time off after the birth of a child, but of those, the vast majority take a week or two, according to a 2011 study of workers at four Fortune 500 companies by the Boston College Center for Work and Family.