In addition to the previous information, we also know that Lady Catherine de Bourgh is the aunt of Mr. Darcy, and that she had already planned a bride for him with class, pedigree and money and that was none other than her own daughter, Miss de Bourgh. That is reason enough to detest Elizabeth after hearing word that Darcy wanted to propose to her.
On the other hand, Caroline was in love with Darcy and always kind of saw herself being married to him. She felt that she was the natural choice for him to marry, and she conducted herself at all times with the attitude of one who is in need to make someone fall in love with her rapidly. For this reason, knowing his interest in Elizabeth, both women detested her.