Carrie is a young woman trying to make her way in the big city. On her own for the first time, she is not sure how to behave. She wants to get a job so she won’t be stuck in the small town forever.
When Carrie is traveling, she notices a man behind her but she does not talk to him until he talks to her. Carrie is inexperienced, and she is not sure how to handle the man.
For some time she had been conscious of a man behind. She felt him observing her mass of hair. He had been fidgeting, and with natural intuition she felt a certain interest growing in that quarter. (ch 1, p. 3)
Drouet dominates the conversation, because he soon realizes she is just an ignorant country girl and he can further dominate and take advantage of. His relationship with her remains dominant.
When Carrie is looking for a job in chapter 3, she is turned down and thus dominated by man after man. As a woman, she does not have the work experience or skills. She has not been trained. It is next to impossible for her to succeed on her own.
Consider this exchange between Carrie and a man she asks for work.
"Well, if I were you," he said, looking at her rather genially, "I would try the department stores. They often need young women as clerks." (ch 3, p. 12)
The man has nothing for her, because she has no skills. Yet he is able to direct her to possible work, in a domineering, disinterested sort of way. He is genial, because she is a pretty young lady.