In the case of Aaron et al. v. Cooper et al., 1958, the U.S Supreme Court ruled that states and school districts must comply with federal court orders to desegregate schools immediately, rejecting arguments for gradual implementation. The Little Rock School Board had previously been ordered by a lower court to integrate their schools following Brown v. Board of Education but sought delay due to opposition from state officials and local citizens in Arkansas who were resisting integration efforts. However, this request was denied by both the district court and on appeal at the Supreme Court level which held that constitutional rights cannot be compromised because they are met with hostility or inconvenience; thus reinforcing its commitment towards ending racial segregation in public education as mandated under Brown v. Board of Education ruling.

In the dissenting opinion of Aaron et al. v. Cooper et al., Justice Frankfurter argued that the Supreme Court should not have taken up this case because it was a matter for local courts to decide, and there were no significant federal issues at stake. He believed that by intervening in such cases, the Supreme Court risked overstepping its constitutional role and undermining its own authority. Furthermore, he contended that even if there were valid reasons for intervention, this particular case did not warrant it as it involved an ongoing process of desegregation which required time and patience to be successful. The majority's decision to force immediate integration could potentially lead to more harm than good by inciting resistance and hostility among those opposed to desegregation.