According to the ruling in the Plessy v. Ferguson case, why was the segregation acceptable?

The Supreme Court ruled in the Plessy v. Ferguson case that segregation was acceptable as long as the facilities for African Americans were "separate but equal" to those of white Americans. This ruling established the legal precedent for segregation in public facilities in the United States, leading to the establishment of "Jim Crow" laws that enforced segregation in many states.