What happens to the rug in "Barn Burning" and how does Major de Spain react?

Ab Snopes deliberately soils the rug. Before he enters the de Spain house, he steps in horse manure, which he refuses to clean from his boot. Once inside the house, he grinds his boot into the expensive carpet and stains it.

Major de Spain takes the damaged rug to the Snopes' cabin and demands that they clean the rug. In another act of provocation, Ab instructs his wife to wash it with harsh lye soap, which completely ruins the valuable carpet.  As a result, Major sues Ab for damages, asking that an additional 20 bushels of corn be awarded to him, and the judge grants his request. Meanwhile Ab, who is outraged by this judgement, has countersued, declaring that 20 bushels is too many, and the judge agrees. However, the judge rules that Ab is responsible for the damages. Resentful, Ab decides he will burn the major's barn.

Why is the damage to de Spain's rug important in "Barn Burning"?

Sarty notices that his father steps in a big pile of horse droppings on his way to the big house, though Ab could easily have avoided the pile. Despite the black servant instructing him to "Wipe [his] foots," Ab pushes the door and the servant away, and strides onto the pale rug inside the foyer without hesitation. When Ab learns that Major de Spain is not at home, he turns (not even acknowledging Mrs. de Spain, as courtesy would dictate), pivots, and "drag[s]" his "stiff foot [...] leaving a final long and fading smear" across the rug. Ab only stops to scrape the bottom of his boot on a fence after they have already left the house, the door closing on the sound of the lady of the house "wail[ing]" hysterically as a result of the damage to her carpet. This episode shows us just how disrespectful—how willfully malicious, in fact—Ab really is. He could easily have avoided the droppings on the ground; he could easily have scraped his shoe off before entering the house. He chooses not to because he wants to show his disrespect. This is a good example of indirect characterization: we can develop an understanding of the kind of person Abner Snopes is from his conduct here. His behavior both before he stains the rug and after it is indicative of one who has no respect for other people and cares only about himself and his own pride.