I completely agree that the Confederate Battle Flag should NOT be flown on public (Government) property, but not for the same reasons you do.
Not everything is as black and white (pun NOT intended) as some people would like to believe, and you cannot look at historical events through the prism of modern knowledge and understanding and judge the actions and convictions of people who lived in a era so far removed from anything contemporary as to be for all intent and purpose, an completely alien culture. It is unfair to make a judgement on the actions of a historical figure without also taking into account the context of the times that figure lived in.
The slaveholding states believed that the rights guaranteed to the states by the Constitution had been repeatedly violated through Federal dictation, and those states' sovereignty having been repeatedly undermined by contradictory laws enacted by other states. They were not wrong, at least not technically.
But it's not easy to hold the moral high-ground of defending states' Constitutional rights when you're simultaneously trying to defend a state's right to practice something as abhorrent as human slavery.
The war actually started when U.S. soldiers refused to vacate a military installation on what South Carolinians saw as their own sovereign territory. Again, they were not wrong. South Carolina had, using excerpts from the Declaration of Independence as precedent, lawfully seceded. As far as they were concerned, they were no longer part of the United States, and they had every right to demand those soldiers should pack up and go that Washington had to demand of the British army the same thing 70 years earlier.
TL;DR version:
1. Flying any flag, logo, or emblem of a defeated and/or defunct nation on public (Government) property is simply not a defensible act.
2. Stop Monday morning quarterbacking the Confederacy, you weren't there.
