Of course, any work of literature has a number of themes that can be identified, so clearly you need to widen the scope of your question to include a range of possible responses. One theme that is obviously evident in this story, primarily through the character of Abner Snopes, is that of rage and anger. Abner is a character who is so quick to take offence over any possible altercation with others, but particularly with those who are socially above him. This anger finds physical form in the literal flames of the barns and property that Abner burns as an expression of his rage and resentment. He is a character who appears to be trapped in a state of constantly achieving revenge against his superiors for supposed wrongs that they have caused him. It is important to note that this anger has resulted in the unhappiness of his family and their constant itinerant state.
Abner is not the only character to display anger, of course, but there is a contrast made between Abner and characters such as Major de Spain and Sarty, because they have reason for their anger. A life that is dominated by anger, as in the prime example of Abner Snopes, is shown to be a life that destroys both self and those closest to you. Ironically, in burning down the barns of others, Abner only serves to metaphorically burn down and destroy his family, by providing his son with the impetus he needs to defy him and leave.