Critics often associate Faulkner's portrayal of the Snopeses with his perception that the "New South" following Reconstruction has lost its values. Consider this proposition with regard to "Barn Burning."

One way to approach this question would be to consider the father's malevolence as an expression of the crumbling Southern social system. The Snopeses are clearly at the bottom of white society, and the father's anger is directed less at anyone in particular than at the world at large. There is little else to explain the father's treatment of the rug other than his resentment of his social position and his determination to make people like De Spain pay, however he can.
Another way of connecting "Southern values" to the story is to consider the notion of family and how the Snopeses are absolutely ruled by the father. The boy's decision to betray his father can be seen as a recognition that Southern patriarchy, at least as it manifests with the Snopeses, has become so rotten that it necessarily must turn against itself.
A third way of approaching this topic would be to consider the importance of history in Southern society and the degree to which stories about the Confederacy are able to form a set of values for society. The boy is named for the fabled Colonel Sartoris, but his father's exploits in the war as part of Sartoris's cavalry were more mercenary. By the end of the story, the boy comes to realize that the "honor" his family attributes to war service is a kind of lie or fable, standing in stark contrast to the violence and hatred of his father, who would coerce him into helping him commit arson.