There are a few ways to look at this antagonist thing. The first would be to say that Henry’s literal antagonist is the whole of the Confederate army. This is the thing that can cause him the most harm and that stands in his way; it is also the thing that he must fight in order to win his "manhood."
The same can be said of Henry himself. He is his own worst enemy. It is his fear and cowardice (and occasional paranoia) that keep him from accomplishing his goal of courageous behavior.
While we’re at it, a good case can be made for the view that war (and all its attributes) is Henry’s worst foe. This would encompass his fear, the Confederate Army, and all the death and destruction that plague the novel.