The narrator says that it wasn't chance that led Daniel's family to the black hair care business: many South Korean immigrants, including Dae Hyun's cousin, own black hair care stores. The South Korean dominance of the market began in the 1960s, when South Korea banned the export of raw hair for wigs, and the US simultaneously banned the import of wigs containing hair from China. This meant that South Korea became the sole manufacturer of wigs, and eventually, this dominance expanded to the black hair care market in general. Now, it's estimated that South Korean businesses control 60-80 percent of the market. Dae Hyun isn't aware of any of this; he just knows that his children will do better than he did.
Again, this history shows that even if there's animosity between South Koreans and African-Americans, the two cultures are still intrinsically linked. Further, that link represents several facets of the American dream for both cultures (financial success for Koreans, and association with European standards of beauty in the form of relaxing chemicals for African-Americans). This shows that the American dream also isn't something that exists just on an individual level.