QUEZON CITY, Philippines—Son Bum-sik takes credit for coining the term Kopino. He uses it to describe a person of mixed Korean and Filipino ethnicity. In 2006, he opened a small shelter and school for such children whose mothers can't afford to take care of them and whose fathers are nowhere to be found.

As a South Korean, "I feel responsible," says Mr. Son, 50 years old. "Some Korean men take no responsibility if they get their Filipino girlfriends pregnant."

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