Plessy vs Ferguson

In 1890 a new Louisiana law required railroads to provide “equal but separate accommodations for the white, and colored, races.” However, when The conductor of the train collected Plessy he told the conductor that he was 7/8ths white and 1/8 black, he was advised he needed to move to a coloreds-only car. Plessy said he resented sitting in a coloreds-only car and was arrested immediately.

You may be looking at Plessy thinking that he is a white man but anyone with one drop of non-white blood was classified as “colored” under the Louisiana code

while the object of the Fourteenth Amendment was to create "absolute equality of the two races before the law," such equality extended only so far as political and civil rights (e.g., voting and serving on juries), not "social rights" (e.g., sitting in a railway car one chooses). As Justice Henry Brown's opinion put it, "if one race be inferior to the other socially, the constitution of the United States cannot put them upon the same plane." Furthermore, the Court held that the Thirteenth Amendment applied only to the imposition of slavery itself.

We consider the underlying fallacy of [Plessy’s] argument,” Justice Henry Brown wrote, “to consist in the assumption that the enforced separation of the two races stamps the colored race with a badge of inferiority. If this be so, it is not by reason of anything found in the act, but solely because the colored race chooses to put that construction upon it.”

https://www.thirteen.org/wnet/supremecourt/antebellum/landmark_plessy.html