According to the Supreme Court, why was the doctrine of "separate but equal" no longer acceptable?

Decided in the case "Brown V. Board of Education of Topeka," the notion of "separate but equal" was no longer acceptable because this notion is inherently unequal. By segregating schools based on race, a divide between the races was produced. Specifically, black school children, even in schools that were "materially equal," had more issues of feeling inferior to whites and being looked down upon by them. This violated the 14th Amendment's Equal Protection Claus.