In re Gault
In the Court's opinion, Justice Fortas wrote that without these due process rights, a person cannot get a fair trial, no matter what age they are.  The Fourteenth Amendment says that "no state can take away any person's "life, liberty, or property, without due process of law; nor deny to any person ... the equal protection of the laws."  Since juvenile courts could take away children's freedom by sending them to juvenile prisons, they needed to give juvenile defendants full due process rights.  They also needed to give them "equal protection of the laws"  the same protections an adult at risk of going to jail would get.