Confederates were inherently conservatives and reactionaries, which has always occupied the "right wing" of the left-right political spectrum as used in modern history. They resisted the progressive (at the time) end of human enslavement/forced labour on just the basis of skin colour.

Of course the US federal government failed to properly dispossess Southern slavers of their property to redistribute to the formerly enslaved population, instead opting to do nothing and allow the North & South to continue white supremacy through unequal enforcement of laws, Jim Crow, lynching blacks, prison slave labour (hence the unequal application of state violence, policing, and unequal sentencing of blacks which is an ongoing problem).

The more time passes since the so-called "end of slavery", the easier it is to deny reparations despite the enormous disparity in generational wealth condensation enabled by 200 years of slavery and 150+ years of institutional and societal racism and kicking the can down the road.