Segregated schools created promote the perception that the Blacks students are 'somehow inferior' compared to the white students, which make them get lesser quality schools compared to white students.
When black students came into school with this initial perception, there would be a high chance that they would be discouraged right from the start to compete with the white citizens after they graduate, which would widen the economic gap between the two populations.
In my opinion, the Court recognized the huge psychological impact that segregated schools had on children who attended them because of the rising cases of troubled children who went to segregated schools. Also, several studies have shown the actual effect of segregation to children.