The townspeople of Jefferson consider Miss Emily Grierson's relationship with Homer Barron a disgrace because she is courting someone well below her social status. Miss Emily hails from a prestigious family and is considered a member of the southern aristocracy, while Homer Barron is simply a northern day laborer. The citizens believe that Miss Emily is forgetting her noblesse oblige and find it disgraceful that she would entertain a man of Homer Barron's caliber. The ladies of Jefferson also feel that Miss Emily is setting a bad example to other girls by dating Homer Barron, and they eventually petition a Baptist minister to pay her a visit to discuss her relationship.
Essentially, the traditionalists of Jefferson consider Miss Emily's relationship with Homer Barron a disgrace because they feel that he is significantly below her social class. They subscribe to traditional southern culture, where prestigious families only marry people among their social class. Although they believe that Miss Emily holds her head a "little too high" and resent her for acting superior, they hypocritically hold her to that high standard by criticizing her for dating a man outside her social class.