Final answer:
The provided information does not contain details about Mrs. Mogson or her reasons for hating Romain, so it's not possible to explain her feelings within the context of these texts.
Step-by-step explanation:
The question seems to revolve around a character named Mrs. Mogson and her dislike for an individual named Romain. However, the information provided does not contain any details regarding a Mrs. Mogson or her feelings towards Romain. Instead, the various excerpts discuss other characters and their interactions or personal feelings.
For example, Mrs. Miller expresses disappointment with Rome, Randolph cites deeper hate each day, Winterbourne contemplates his past actions towards Daisy Miller, and various characters struggle with emotions ranging from hate to affection and inner turmoil.
These narratives explore different emotional states and conflicts but do not specifically address Mrs. Mogson's hatred for Romain. Consequently, without the proper context from the text regarding Mrs. Mogson and Romain, it is not possible to explain what action or event caused her hatred.