What was the Supreme Court's justification for overturning the separate-but-equal doctrine?

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The Supreme Court's justification for overturning the separate-but-equal doctrine in Brown v. Board of Education was that segregated schools stigmatize minority children and are inherently unequal. The Court determined that even if the physical facilities were equal, the doctrine of separate but equal was inherently unequal and violated the Equal Protection Clause of the Fourteenth Amendment.

What Was the Supreme Court's Justification for Overturning the Separate-But-Equal