In chapter 2, Tom and Nick head to the city together, and Tom wants Nick to meet his mistress, Myrtle. Nick spends part of the evening talking to a woman named Catherine, Myrtle's sister. She fills Nick in on Tom and Myrtle's relationship, mentioning that the two would get married if Tom could get a divorce. Catherine explains that since Tom's wife is Catholic, he is having a hard time leaving her; Nick is Daisy's cousin, so he knows that she isn't Catholic and is surprised by the "elaborateness of the lie." Tom has seemingly concocted this story to keep Myrtle around, and she believes that one day the two of them will leave their spouses and marry each other.
Time passes at the party, and for whatever reason, Daisy comes up in a conversation between Tom and Myrtle. Tom has evidently forbidden Myrtle to say Daisy's name, and Myrtle taunts him by repeating the name "Daisy" over and over. In response, Tom unexpectedly uses his open hand to break Myrtle's nose. Blood goes everywhere.
This act shows that Tom is a violent man with no respect for Myrtle. He is using her for his own pleasures, and he does not love or respect her, despite what she believes about their future together. Instead, Tom's alliance is clearly with his wife Daisy, which is why he refuses to allow his mistress to speak of her. Despite his affair, this scene proves that Tom holds Daisy in a higher regard than Myrtle, and he doesn't flinch to use violence to remind Myrtle where his loyalties lie.