I'm going to put my history major hat on here for a sec and try and explain this as best I can.
There are a lot of reasons for the reverence of the South, but one major reason is the myth making and narrative shaping Confederate and Southern groups did after the war, from the mid to late nineteenth centuries and into the early twentieth centuries. There's a really good book about it called Race and Reunion: The Civil War in American Memory. A quote from that book lays it out pretty well: “In many ways, this is a story of how in American culture romance triumphed over reality, sentimental remembrance won over ideological memory.” Confederate groups, from veterans to widows to politicians, developed a sentimentalism toward the South. The North helped a lot in this, honestly, as there was a widespread reconciliation movement, as white Americans attempted to move past the Civil War. So you would have veterans from both sides attend events remembering the battles and trying to put their differences aside, basically talking about the 'nobility' and 'determination' of the combatants while ignoring slavery and ignoring African Americans. Race and slavery had been such a dividing force between the North and South so remembering that didn't suit the reconciliation they were going towards, and instead they left ideology behind so they could unite as Americans, which also fit well with the burgeoning American nationalism. Once Reconstruction ended and the Jim Crow laws were enacted, African-Americans were by and large disenfranchised and widely discriminated against.
Another major reason was the "Lost Cause" mythos built up following the war. First it was focused on building up Robert E. Lee and talking about the war as a cause that could be defeated only by the overwhelming industrial might of the North, and that Southern resistance had been hard fought in spite of the odds. They also didn't stress the cause of slavery as much and instead focused on white supremacy, which they could keep fighting for by resisting Reconstruction, and through that they created a victory narrative in which they successfully fended off the North in allowing African-Americans to 'rule'. In the immediate aftermath they also created their own histories to combat what they saw as false Northern histories, forming groups and writing books from the Southern perspective. And they built statues and monument in the late 19th century and early twentieth century to local soldiers and people like Robert. E. Lee. When his statue was unveiled some in the North protested it, as they saw didn't like "liberal display of rebel flags" or the cult that had grown up around Lee, even in the North.
Really, it has to do with the fact that people in the South continued to celebrate the South in ways that could deem the South's cause as more noble than it was and could ignore sticky issues like slavery while stressing things like white supremacy, which even many in the North agreed with because of the widespread racism. And they shifted towards talking and writing about the conflict as one of ideals about states rights vs. federalism. As the world wars passed and the Civil Rights movement kicked off, the flags and Confederacy became aspects of Southern heritage that white Southerners used to counteract the calls for integration and equality. Though they didn't advocate for slavery, they still clung to the white supremacy aspects that were trumpeted by the Confederacy.
The Confederacy lost the Civil War but they won the battle over the memory of the Civil War. In this case, history was not written by the victors but by the losers. So now you have a fairly widespread belief that the Civil War was over states right and federalism, while ignoring that the state right they really cared about protecting was the right to own slaves. Basically, the reconciliation of the white Northerners and Southerners allowed the South to shape the narrative of the Civil War in a way that better reflected on them, and many people still buy into those ideas and the imagery associated with them.