Chief Justice Warren believed that public education was more important in the 1950s than it had been in the 1860s (when the 14th Amendment was ratified) or the 1890s (when Plessy was decided) because it was much more widespread and therefore played a bigger role in creating and shaping modern society.
Warren pointed out that public education had been very limited in scope in the 1800s. He said that
In the South, the movement toward free common schools, supported by general taxation, had not yet taken hold. Education of white children was largely in the hands of private groups. Education of Negroes was almost nonexistent, and practically all of the race were illiterate.
Because of this, the 14th Amendment never addressed the issue of public education. But now, in the 1950s, public education had become pervasive and very important. As Warren said,
Today, education is perhaps the most important function of state and local governments. Compulsory school attendance laws and the great expenditures for education both demonstrate our recognition of the importance of education to our democratic society.
Warren was arguing that public education was not prevalent in the 1860s and was therefore not addressed in the 14th Amendement. But because it was very important in the 1950s, it had to fall under the amendment's guarantee of equal protection.