Did they act or campaign to make things worse for their fellow man (and woman)? In other words, did they simply act in the context of their time period, as other men in their position would, or did they specifically act to curtail the rights of others. This makes it very easy for me to condemn symbols of the Confederacy, because they specifically acted to preserve slavery.
If anyone believes the Confederates did not rebel and fight specifically to preserve slavery, they should read the words of the seceding states: https://www.battlefields.org/learn/primary-sources/declarati...
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Taking it back to your question about Mexico: War is terrible, and flags are used in war. Flags are used after the war is over to show their solidarity with the principles of one side or the other. The flag of Mexico was primarily just a marker to say "We are Mexico"
Some people associate the confederate battle flag with a spirit of rebellion, and that's understandable. But other people associate it with hatred. You don't get to choose how someone else will understand it and be affected by it. It's hard to be a grown up, but part of it is deciding how much you care about offending other people.