Other:
Both the Confederate and US flags were flags of slavery.
That argument just doesn't hold any water. Yes, the U.S. flag has flown over just as many (well, more, really) atrocities. But the U.S. flag stands for so much more than that.
In contrast, the only relevance of the Confederacy is that it attempted to break away from the U.S. out of fears that it would lose slavery. Perhaps if the South had won the war, gone independent, but later cleaned up its act and became a freedom-loving first world country with the same flag, the Confederate flag would not be an offensive symbol. Maybe Confederate soldiers would have helped storm the beaches at Normandy under that flag. But that's not what actually happened, thus the Confederate flag only stands for a few elites who wanted so badly to keep owning people that they committed treason, and the legions of impressionable poors that blindly followed them.
It wasn't just the elites who had slaves. Even among poors who had no slaves support for the Confederacy isn't evidence of being impressionable or blindly following. Aside from fears about a race war, they didn't want to have to compete for jobs or land or status with blacks. And they sure as hell didn't want the Yanks telling them what to do, and so many were willing to fight to defend their homeland against those they saw as meddling invaders.
As to the question of what the flag means, there's no way it's going to only mean one thing. It depends on where and what it's used for.
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