How does segregation violate the constitution?

Separate but equal was a legal doctrine in United States constitutional law, according to which racial segregation did not necessarily violate the Fourteenth Amendment to the United States Constitution, which guaranteed "equal protection" under the law to all people. Separate but equal

In Brown v. Board of Education of Topeka in 1954, the court decided that "separate educational facilities are inherently unequal," and thus violated the Equal Protection Clause of the 14th Amendment. The ruling overturned Plessy and forced desegregation.