Jim Butcher's decision to join Sweden's army of "latte dads" last year didn't win him any popularity contests with family and friends back home in the U.K.

"When I told my friends in England, they spat up their tea," said the 35-year-old head of communications for digital-music company Spotify Ltd., which is based in Stockholm.

"They thought my out-of-office reply—that I was gone for six months—was a joke." His father, a self-employed bricklayer, was concerned his son was jeopardizing his career.

But Mr. Butcher had a serious agenda for his half-year hiatus: Spending uninterrupted time with his newborn daughter.

Sweden's paternity-leave benefits, enjoyed by citizens and foreign residents alike, are the most generous in the world—and a debate is under way nationwide over whether to extend them even further. Sweden should require men to take a minimum of three months' leave, instead of the current two months, some politicians argue.