Good point, I found on Google that segregation violated the Equal Protection Clause of the Fourteenth Amendment. Get a load of this, but I honestly made a gut feeling that I honestly thought (with prejudice but I didn't post it anyways) that segregation "was constitutional". But it never was, which I'm glad I did my google search.
But why did they have segregation in the first place, if it was unconstitutional?
https://www.law.cornell.edu/wex/separate_but_equal