First, we have to realize that there is no objectively correct answer to this question. We cannot know for sure why the Civil War continues to have importance for Southerners. That said, we can speculate. I would speculate that there are two main reasons why the war is still important to Southerners.
First, it continues to be important because the South lost. Because they lost, they feel the need to continue to honor the effort that they made. They need to feel like the war was important and that it was a war that was worth fighting even though they lost.
Second, and perhaps more importantly, it is because the South has been in some ways subordinate to the North ever since the war. The South is still poorer than the rest of the country. Northerners have often looked down on Southerners as being somewhat backwards. People also think of the South as a hotbed of racism. Because the South is seen this way, Southerners can feel defensive and can feel that it is important to show that they are just as good as the North. One way to do this is to dwell on the war and to see it as an example of how the North has oppressed them.
These are, in my view, reasons for the South’s attitudes toward the war. However, there is no way to prove that these views are correct.