Final answer:
Millicent wanted to move out because she felt her privacy was being invaded due to the close proximity to her male neighbor, which made her uncomfortable.
Step-by-step explanation:
Millicent expressed her desire to move out of the room she was supposed to share with Agatha because she felt uncomfortable with the arrangement. In particular, she mentions her room being quite small and the wall-paper pattern continuing from her room into his, giving the impression that it once might have been a single room. This proximity to a male neighbor, who she refers to as possibly being the 'younger son of a baronet', made her uncomfortable to the extent that she considered speaking to the landlady about it. Her expressed discomfort suggests she values her privacy and the traditional norms of modesty and separation between unmarried men and women.