At the beginning of the story, we are told that Ulrich von Gradwitz has always, since he was a boy, hated and considered Georg Znaeym a mortal enemy. Ulrich patrols the woods and wishes that he would come face-to-face with Georg, in a "dark, lone spot ... with none to witness." The implication here is that Ulrich would like to kill Georg, especially in the woods, where it is dark and there will be no witnesses.
However, when Ulrich does come face-to-face with Georg, each with a rifle in hand, he finds himself unable to pull the trigger. The author, by way of explanation, writes:
A man who has been brought up under the code of restraining civilization cannot easily nerve himself to shoot down his neighbor in cold blood and without a word spoken, except for an offense against his hearth and honor.
In other words, Ulrich finds himself...
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unable to shoot his enemy because society has conditioned him to believe that it is wrong to kill a man, especially a man who is one's neighbor, without at least speaking to him first or without a very significant threat to one's home ("hearth") or insult to one's honor. Georg poses no direct threat to Ulrich's home, and he has not insulted Ulrich's honor. And, presumably, Ulrich cannot in the moment think of anything that he might say to Georg which would justify then shooting him dead. Thus, although Ulrich hates George, he has no socially sanctioned reason to pull the trigger.
For these reasons, Ulrich stands as if frozen before Georg, unable to pull the trigger, even though he clearly hates Georg. Before Ulrich can fully rationalize why he is unable to kill his enemy, a "fierce shriek of the storm" causes a tree to topple on top of him and Georg, trapping them both. In this trapped state, unable to move, Ulrich and Georg talk through their differences and come to understand that those differences are trivial. From the reconciliation between the two characters, we can infer that Ulrich, ultimately, could not shoot Georg, simply because the cause of his hatred for Georg was too weak. His hatred for Georg was founded on far too little to justify murder.