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I think the question is slightly ill-posed, because it assumes that before segregation there was integration. That is not the case. Racial segregation existed from the very beginning of black immigration to North America -- but it was originally based on slave status. That is, slaves were legally distinct from freedmen, based on the fact that they were slaves. So segregation on the basis of race alone was a continuation of the policy of segregation, when it could no longer be made on the basis of a state of slavery. The right question to ask, then, is: why did the termination of slavery NOT bring about racial integration? Why, instead, were new laws and policies enacted that preserved the racial segregation that had been present while slavery was legal? Put that way, the answer may be no more complex than that (1) people are slow to change, and (2) they are very resistant to change when it is enforced by military conquest. But I think you can also make a case that the heart of the North was not as strongly attached to the liberation of the black man as might have been thought. Northern society, and particularly the Northern Democratic Party, was very willing to terminate President Grant's cheerless and draining efforts to force the South to change its attitude towards blacks, and, when the opportunity arose with the election of Hayes, Reconstruction was effectively terminated and the job of conversion left undone. Indeed, it's not hard to argue that conditions became a lot worse in the following reaction, and that it would've been much better to be a black man in South Carolina in 1872 than in 1902 or 1912.
Thank you so much!!