Short Answer 
States delayed desegregating schools after Brown v. Board due to the lack of a strict deadline, which allowed for varying interpretations of “all deliberate speed.” Additionally, tactics of massive resistance were employed, including the closure of schools, alongside significant political opposition from Southern officials committed to resisting desegregation efforts.
Lack of a Deadline
The Supreme Court’s ruling in Brown v. Board of Education did not specify a strict timeline for schools to desegregate. Instead, it instructed states to proceed “with all deliberate speed.” This vague phrasing allowed for significant delays in many areas, as states could interpret the timeline at their discretion.
Massive Resistance Tactics
In response to the ruling, some states, particularly Virginia and others in the South, adopted a strategy known as ‘massive resistance.’ This involved drastic measures, including the outright closure of public schools rather than allow them to integrate. This tactic was intended to demonstrate defiance against federal mandates.
Political Opposition
Many Southern officials strongly opposed the desegregation efforts, as articulated in the ‘Southern Manifesto.’ This document, supported by numerous politicians, declared a commitment to resist desegregation “by all lawful means.” Such political opposition further complicated the implementation of the Supreme Court’s ruling and hindered progress toward integrated schools.