Explain how the Supreme Court justified the practice of segregating railroad passengers in Louisiana by race.

In this question, you are referring to the Supreme Court case of Plessy v Ferguson, which was decided in 1896.  In that case, the Court had to decide whether a Louisiana law that required whites and blacks to sit in separate train cars violated the 14th Amendment.  The Court held that it did not.  There were two main reasons for this.

First, the Court said that the 14th Amendment was meant to make blacks...

In this question, you are referring to the Supreme Court case of Plessy v Ferguson, which was decided in 1896.  In that case, the Court had to decide whether a Louisiana law that required whites and blacks to sit in separate train cars violated the 14th Amendment.  The Court held that it did not.  There were two main reasons for this.

First, the Court said that the 14th Amendment was meant to make blacks and whites equal in legal terms, but not in social terms.  It said that there was a difference between making sure that blacks had the right to vote and requiring that they be allowed to sit in the same train cars as whites.  The Court pointed to previous cases, including one in which segregated schools in Boston were found to be constitutional.  The Court held that the amendment was meant

…to enforce the absolute equality of the two races before the law, but in the nature of things it could not have been intended to abolish distinctions based upon color, or to enforce social, as distinguished from political equality…

In saying this, the Court asserted that there was a real difference between political rights such as voting and social rights such as the right to share public facilities.

Second, the Court said that Louisiana’s law did not imply that blacks were inferior to whites.  Instead, it was based only on the idea that the two races were different.  Although the Court did not draw this analogy, we can think of this in terms of having different bathrooms for the different sexes.  Most people do not believe that we imply that women are inferior to men when we set up separate bathrooms for them.  Why, then, would we think that separate facilities imply that blacks are inferior to whites.  The Court said that these laws only labelled blacks as inferior if black people thought they did.  In the words of the majority decision,

We consider the underlying fallacy of the plaintiff's argument 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.

There are, then, two main reasons ways in which the Court justified segregation.  First, it said that the 14th Amendment guaranteed only political rights and not social rights.  Second, it said that it was only in the imaginations of black people that the law implied that whites were superior.