“but why should it fly on government property?”
A state government, Constitutionally, represents the will of the people. Across the nation, for example, old buildings that house seats of government have Christianity chiseled on their walls. This idea of government property being antiseptically cleansed of all hallowed cultural symbols is very new and rejects historical usage. If a state wants to fly the Confederate flag on its property, that is their constitutional prerogative. If a state does not, that is also their constitutional prerogative.
Of course it is their Constitutional privilege. Does that make it right?
If Georgia wants to put a swastika on their flagpole, they could, but it would be the wrong thing to do.
No, the Confederate flag isn’t the equivalent of the swastika, but like it or not, it has been used by many as a means of hatred.
What is the argument to keep it flying on government property?
In the end, the members of government will vote and everyone will have to respect that decision no matter how it turns out.
On a personal note:
I was the first white to be invited to join an all black golf club. I accepted.
A group of 40 of us flew to South Carolina for a weekend of golf. Twice that weekend, trucks with Confederate flags drove by and taunted our group. They were s cumbags trying to use the flag as intimidation.
That was almost 20 years ago and it was when I realized it was time to take the flag down.