According to Justice Brown's opinion in Plessy v. Ferguson, what did he consider segregation to be?

A Fallacy. Justice Brown considered a separation as a form of putting African Americans to the status of inferiority only in their own eyes because of rule "separate but equal" he revoke Boston case upholding segregated schools, dissenter of this was Justice Harlan

Segregation was not inherently a violation of the Fourteenth Amendment because it did not deny services or citizenship rights.

Justice Brown stated segregation is not a violation of the Fourteenth Amendment (which grants citizenship rights) if the facilities are equal. By providing equal access to Constitutional rights even if in segregated facilities, the segregation is allowed. If the laws state for unequal treatment then segregation would be in violation of the Fourteenth Amendment.