The United States’ Constitution is not a very detailed document. It lays out the basic structure of government, and the details are filled in with legislation, and clarified and reinforced by court decisions.
One of the most consequential Supreme Court decisions was the 1896 case of Plessy v Ferguson, which set the precedent that segregating people by race was acceptable.
This meant that every public accommodation had the right to refuse to serve Black Americans, and that even public institutions like schools could be segregated.
While the decision did stipulate that the segregated accommodations be “separate but equal,” the equal part of that equation was often left out.