How did the brown decision lead to conflict between federal and state governments?

Brown v. Board of Ed overturned the Plessy v. Ferguson. It established that the concept of "separate but equal" was unconstitutional and was an example of the argument between whether the national or state government should hold more power. The decision also declared that all states had to desegregate, but, much of the country was still prejudiced, the states strongly opposed of it. They argued that the federal government was intruding on the power of the states.