What was the essence of thurgood marshall's argument in the supreme court in brown vs. the board of education?

Thurgood Marshall's arguments in the Supreme Court case Brown vs. Board argued that segregated schools violate the Equal protection clause of the 14th amendment. Along with this, Marshall argues that the doctrine of "separate but equal", established in the Supreme Court case Plessy vs. Ferguson, has resulted in severe inequality in American society for African-American citizens. He uses examples of different times when African-Americans and whites interact in American society without a problem as a means to strengthen his argument as to why school segregation should end.