Person of race A and race B have two children. People tend to think child 1 is race A, people tend to think child 2 is mixed race AB. In the social sense, it could be said that child 1's race is race A, even though genetically it's probably more like AB.

Another common situation: People of race A think child 2 is race B, people of race B think child 2 is race A. And you can imagine more complex examples with more races and more generations. In this manner the categorization of race is primarily social.