All the Southern state legislatures, with the exception of Tennessee, refused to ratify the amendment, some voting against it unanimously. In addition, Southern state legislatures passed “codes” to regulate the African-American freedmen. The codes differed from state to state, but some provisions were common. African Americans were required to enter into annual labor contracts, with penalties imposed in case of violation; dependent children were subject to compulsory apprenticeship and corporal punishments by masters; vagrants could be sold into private service if they could not pay severe fines.
Many Northerners interpreted the Southern response as an attempt to reestablish slavery and repudiate the hard-won Union victory in the Civil War. It did not help that Johnson, although a Unionist, was a Southern Democrat with an addiction to intemperate rhetoric and an aversion to political compromise. Republicans swept the congressional elections of 1866. Firmly in power, the Radicals imposed their own vision of Reconstruction.
In the Reconstruction Act of March 1867, Congress, ignoring the governments that had been established in the Southern states, divided the South into five military districts, each administered by a Union general. Escape from permanent military government was open to those states that established civil governments, ratified the 14th Amendment, and adopted African-American suffrage. Supporters of the Confederacy who had not taken oaths of loyalty to the United States generally could not vote. The 14th Amendment was ratified in 1868.
This doesn’t answer your question as to why the south didn’t want the 14th amendment, but it sheds light on the ratification process.