The culture of the people of the South, developed over a couple hundred years, was a distinct thing that was largely eradicated by Reconstruction and by the massive casualties that basically destroyed a couple generations (much more so than the North). I think that is what is celebrated and remembered by most Southerners who participate in these events and aren't blatant racists (which is most of them, these days). There are old stories and attitudes (honor, gentility, a certain hospitality and graciousness in guest and host, etc) and cultural artifacts from that culture that are still passed on, and there's also an obvious break where that culture was intentionally destroyed and edited by a victorious North imposing its will on a conquered people. That stings, and it'll always sting for some.

You can condemn it all if you want, because they also had slaves, but Rome had slaves. Egypt had slaves. Multitudes of other societies that we study and appreciate aspects of their culture also had slaves. Imagine if some foreign warlord had conquered Athens in antiquity, burned it to the ground and toppled every stone, and the Athenians were made to rebuild 70's soviet style homes, stop aspects of their culture, and also give up slavery. And afterwords people told them to get over it and stop being upset, because they had slaves and so deserved it. There are probably a few who would dress in togas and do recreations of discourses with Socrates and Plato, but not to memorialize slavery. (Not saying the South was intellectually equal to Athens, just saying both were distinct cultures. )

You can all downvote me into oblivion now. I just think that maybe there were a few nice things about southern culture, not unrelenting evil in every facet, and that's something, that sense of lost good culture, that some decent people miss.