Why did thurgood marshall cite the 14th amendment to argue that segregation in public schools was unconstitutional

Historical context:

Thurgood Marshall argued on behalf of the plaintiffs (black students seeking access to all-white schools) when the cases grouped under Brown v. Board of Education were brought before the Supreme Court in 1952-1953.  At the time, Thurgood Marshall was the head of the Legal Defense and Educational Fund of the National Association for the Advancement of Colored People (NAACP).  

The decision of the Supreme Court in Brown v. Board of Education (decided 1954), agreed with the arguments made by Thurgood Marshall.  The Court ruled that all Americans are entitled to the same civil liberties and equal protections in regard to access to education. Until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.  An older Supreme Court decision, Plessy v. Ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.  In the case of Brown v. Board of Education, that standard was challenged and defeated.  Segregation was shown to create inequality, and the Supreme Court unanimously ruled segregation to be unconstitutional.

The ruling affirmed that the 14th Amendment applies to all rights and privileges of citizens, including access to  education.  Section 1 of the 14th Amendment reads as follows:

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explanation:

the fact that that the teachings on the cosmic order comes from, or through, the heart center