The Lawyer of Linda Brown claimed that those schools were racist and segregated students based on archaic and incorrect beliefs that there is genetic difference between white and black people in which the African-Americans are not as developed. Of course, the supreme court ruled that we are all equal and the schools were forced to put the students together.
Because, the Persians felt that their army could outnumber Greece, also because they might not have known what they were getting into when they attacked the Greek city-states. Hope that helped :D