For the tl;dr crowd, the South wanted to count them as 5/5ths of a person and the North wanted to count them as 0/5ths of a person.
The problem is that the North came around to the right side of things with respect to rights, while the South only wanted slaves counted - not to give them actual rights.
But the fact is, things change. Things changed between the establishment of the constitution and the Civil War, just as things have changed between the Civil War and now. The time for this symbol is gone. If Southerners are the true patriots they claim to be, they'd throw away this symbol to tyranny and rebellion against their country and pledge allegiance to their real flag instead of worshiping the Confederation's rebellious symbol.
As I said, things change. But the South seems to be too stubborn to change fast enough. We in the North are tired of your social heel-dragging trying to keep us in 1950's America. The bottom line is that the world has changed. Fucking adapt, already. Or secede. Don't care which. Just get out of the way.