One problem with these assignments is admixture. Many people have a highly varied ancestry. For example, in the United States, colonial and early federal history were periods of numerous interracial relationships, both outside and inside slavery. This has resulted in a majority of people who identify as African American having some European ancestors. Similarly, many people who identify as white have some African ancestors. In a survey in a northeastern U.S. university of college students who identified as "white", about 30% were estimated to have up to 10% African ancestry.
What is a problem with racial assignments?  How many people have a varied ancestry? When were periods of numerous interracial relationships in the U.S.? Who do many people who identify as white have for ancestors? What percentage of African ancestry were 30% of college students identifying as white estimated to have?