SEOUL—A cultural preference for male children has cost Asia dearly. Count up all the girls who were never born because of selective abortion, victims of infanticide and females who died from neglect and there are upwards of 100 million women missing on the continent today by some estimates.

Not just a human-rights catastrophe, it is also a looming demographic disaster. With Asian birthrates already plummeting, that is tens of millions of women who will never be mothers. The economic and social impact on some of the world’s largest countries is incalculable.

For decades, South Korea was Exhibit A in this depressing trend. By 1990, as medical advances made prenatal sex selection routine, the ratio of male-to-female babies soared in South Korea to the world’s highest, at 116.5 males for every 100 females.

Then something unusual happened. South Korea did a U-turn.

In one generation, South Korea has gone from a society where sons are prized to one where daughters are just as eagerly received. Turbocharged industrialization, urbanization and education, along with a feminist revolt, wiped out centuries-old practices in which a son was essential to inherit property, worship ancestors, care for parents and continue the family lineage.