My two cents for what it is worth, the man Alvin Cobb believed he was fighting to protect his home.
When the Yankees destroyed Cobb's home, it would appear that your ancestor was so strong willed that he did not break, he fought even harder.
If he had fought for the Union, Cobb would have been highly decorated.
One of my long lost cousins made a comment about my ggg grandfather calling him "a hot headed rebel," to which I replied that "our family considered him loyal to the family." Of course I was never bothered with that man again.
It kind of depended on what side you viewed it from. Hindsight as the old saying goes is 20-20 and it sounds like your ancestor Alvin Cobb was caught up in the times.
If he were my kin, I would track down his grave and make sure that man had a marker. He was a person of conviction and not afraid to stand and fight regardless of what the folks nowadays say about him.
Good luck in your search.