Mark writes to Juliet, annoyed that she doesn't want to go to a play with him. He says he'll do anything to get her out of the house on a date. Juliet writes back and invites him to the British Museum with her, as she has an appointment in the Reading Room. He rudely refuses, tells her to come have lunch with him, and says he's done being nice.
When Mark rudely refuses Juliet's invitation and won't accept her desire to stay in, it again indicates that he doesn't respect her as an individual capable of making decisions. Instead, he'd like to control her and dictate everything she does.