Segregationists wanted to impeach Earl Warren because, through his leadership on the U.S. Supreme Court, the segregation of public schools was ruled unconstitutional in a unanimous decision. This prompted legislation that banned segregation in other areas as well.
The first case that Warren considered as a Supreme Court justice was Brown v. Board of Education in 1954. Biding his time until his appointment was confirmed by the Senate, Warren encouraged the justices to find common ground on the issue. Ultimately, he persuaded them to reach a consensus by arguing that the only way to uphold segregation was by believing in the inherent inferiority of blacks, and only Supreme Court unanimity would overcome strong resistance to desegregation in the southern states. Segregationists who opposed the ruling initiated the "Impeach Earl Warren" movement because they rightly perceived him as the decisive force behind the uniting of the court in the decision.
The decision in Brown v. Board of Education exacerbated civil rights turmoil in the 1950s and 1960s. However, it also prompted other civil rights legislation such as the Civil Rights Act of 1964, which outlawed discrimination and guaranteed all citizens equal protection, and the Voting Rights Act of 1965, which forbade discrimination of voters.