Ryota (Masaharu Fukuyama) has raised Keita (Keita Nonomiya) as his son, only to learn that babies were switched in the hospital, in “Like Father, Like Son.” (IFC Films)

The setup of “Like Father, Like Son” seems like it would be heart-wrenching: Two couples, each with 6-year-old sons they cherish, discover that a hospital mix-up switched their babies at birth.

Yet this Japanese film is more of a head-scratcher than a tear-jerker. Whether because this mistake has, apparently, been a problem before — at least in the somewhat backward hospital where the births took place — or because of something deep in the personal character or national culture of the people involved, all the parents seem more dazed than wrenched by the news.

Sure, they’re all mildly worked up. One father is practically licking his lips at the money he might get from a settlement. But generally, their reactions seem strangely subdued at the decidedly mixed prospect of losing the child they’ve raised, even as they’re reunited with lost flesh and blood.

Stranger still is how the kids themselves — once the families agree to attempt a tentative trade — don’t seem very traumatized. This contributes to a sense that the story is a construct, a puppet show meant to deliver a message rather than to shed light on actual human behavior. At no point does anyone consult a social worker, for instance, about how to handle the mess. Shouldn’t that be one of the first things you do? There are lots of lawyers here, but no therapist.

On one level, the story seems like it’s about paternal nature vs. nurture. The first boy, Keita (Keita Ninomiya), has been living in a nice apartment with his well-to-do but distant and demanding architect father, Ryota (Masaharu Fukuyama). The other child, Ryusei (Shogen Hwang), is one of five living in a crowded and cluttered, yet cozy home tucked behind a ratty appliance shop. His father (Riri Furanki) is an absent-minded goofball, an overgrown kid himself.

For what it’s worth, the differences between the mothers (Machiko Ono and Yoko Maki) are less pronounced. But the story isn’t really about them.

Filmmaker Hirokazu Kore-Eda invites us to ponder two things. Will the children grow up to become more natural fits with their real fathers? Keita is a charming boy, but because he doesn’t possess Ryota’s skill at the piano, he’s something of a disappointment. The other question: Is being a father defined by DNA or by love? Put another way, is your son the one you sire or the one you raise? Perhaps, the film suggests, it’s a bit of both.

Kore-Eda even introduces us to Keita’s grandfather (Isao Natsuyagi), another emotionally distant man, just to drive home his point about the apple not falling far from the tree.

It takes a while for the film to tease out all of these ideas. But by the time “Like Father, Like Son” does, it starts becoming a far more interesting tale. The emotional detachment in the way the parents handle the switch is still unsettling, as is the way the two boys tolerate it. One of them runs away to be with his real parents (or at least the only ones who are “real” to him). But in general, the speed and stoicism with which Keita and Ryusei adjust to the familial maneuvering is, quite frankly, weird.

At the same time, “Like Father, Like Son” grows on you, subtly and over time. Just as with the unexpected realignments forced on its characters, it may be difficult to fall in love with the movie, but eventually you do warm up to it.

★ ★

Unrated. At Landmark’s E Street Cinema. Contains nothing objectionable. In Japanese with subtitles. 121 minutes.