The Browns and other families were asking the supreme court to ALLOW AFRICAN AMERICAN CHILDREN TO THE SCHOOL OF THEIR CHOICE.
Linda Brown wanted to attend the school that is nearer to her home. Unfortunately, the school denied her permission to attend said school and referred her to another school that is farther from her home. Her desired school only catered to white people.
The family wanted the school to accept Linda Brown as their student w/o prejudice to her color. They wanted to have the school be a non-segregated one where everyone is welcome regardless of color.