How was Reconstruction a failure?
Reconstruction was a failure in that it failed to ensure civil liberties for former slaves or provide a life for them which came anywhere close to equality.
Slavery was ended by the Thirteenth Amendment (NOT, contrary to popular myth, by the Emancipation Proclamation.) However, once freed, slaves had no means of providing for themselves or their families or of ensuring equality of treatment. Congress attempted to remedy this first by creating the Freedman's Bureau and also by passing the Fourteenth Amendment which presumably gave them the equal protection of the law and the Fifteenth Amendment which presumably gave them the right to vote.
Both Amendments were circumvented with abandon. The U.S. Supreme Court in Plessy vs. Ferguson in 1896 sanctioned "separate but equal" facilities. it was not until 1954 with Brown vs. Board of Education that the heinous doctrine of "separate but equal" was abrogated. Southern states imposed poll taxes, literacy and residency requirements, among others to keep blacks from voting, and also listed certain crimes assumed to be common among Blacks (wife beating, public drunkeness, etc.) as disqualifications for voting. Vigilantes such as the Ku Klux Klan terrorized Blacks to prevent their exercising their rights as U.S. citizens. Rather than deal with these injustices, Congressional Republicans agreed to withdraw troops from the South in 1877 to ensure the election of their candidate, Rutherford B. Hayes, to the White House. Reconstruction was left only partially completed, and true rehabilitation did not occur for another one hundred years.