One of the greatest mistakes the Supreme Court has made in regards to minority rights was upholding the doctrine of separate but equal under Plessy v. Ferguson. Subsequently, Louisiana passed the Separate Car Act which required separate accommodations on train rides between whites and blacks. In response, the Committee of Citizens was formed to challenge the law under Homer Plessy who was one-eighth black.
Plessy went into the "whites only" section of a train ride an was promptly arrested. Plessy appealed his case until it was eventually heard by the Supreme Court after being decided against his favor in the Louisiana State Supreme Court. The Supreme Court upheld Louisiana's law as long as the facilities were equal and didn't classify any race as inferior to another. The case allowed for states across the South to create facilities segregated by race, and it became obvious to many that the facilities weren't actually equal.
It wasn't until the 1930s when the court expressed a hint of regret. The Supre Court reexamined the doctrine of separate but equal in Missouri ex rel. Gaines v. Canada, in which the court struck down Missouri's plan to pay out-of-state tuition for blacks to attend law school, for the state didn't have at the time since it violated the Equal Protection Clause of the Fourteenth Amendment. The court went further in the 1950 case of Sweatt v. Painter in applying the Equal Protection Clause with regards to law schools and the separate but equal doctrine.
H.M. Sweatt applied for the University of Texas law school because there was no law school in Texas that admitted blacks. In response, he sued Texas in order to be admitted to the school. The state aimed to end the lawsuit by building a new law school in order to meet Sweatt's demands. The Supreme Court ordered Sweatt to be admitted to the University of Texas law school as the newly constructed law school for blacks wasn't actually equal to the law school serviced for whites in terms of library size, faculty members and funding.
The court finally revisited the separate but equal policy in Brown v. Board of Education which examined the effects of the policy on public schools. In an unanimous ruling, the court struck down the separate but equal doctrine for schools, even if the facilities were equal, because the segregation itself violated the Equal Protection Clause in the 14th Amendment. The opinion by the Supreme Court was reached after thorough scientific investigation found that segregation in schools had major negative effects on the black students attending affected areas. The decision not only ended segregation in public schools but also the half-century policy of Jim Crow laws across the southern states.