In chapter 2, Tom and Nick take a train to New York. On their way to New York, they pass a depressing, impoverished place known as the "valley of ashes." This is where Tom's current mistress (Myrtle Wilson) lives with her husband. When the train stops at the aforementioned valley, Tom "jump[s] to his feet and ... force[s]" Nick from the train. Tom says to Nick, "We're getting off!" and then tells him, "I want you to meet my girl." Tom's forcefulness here is in part because he "tanked up a good deal at luncheon," meaning that he had drunk a lot of alcohol at lunch. He is also simply excited at the prospect of soon meeting up again with his mistress to continue their illicit affair.
One reason Tom is so insistent that Nick should meet Myrtle is simply because he wants to show Myrtle off to Nick. Myrtle is described as a sensuous woman with a body that is "continually smouldering." She is a prize that Tom likes to show off to boost his own ego and to validate his own sense of masculinity. Tom takes great pride in his masculinity, which he seems to validate by having lots of affairs with women.
Tom takes Nick to Myrtle's husband's garage, to arrange a rendezvous with Myrtle. While at the garage, Tom also seems to take great pleasure in humiliating Myrtle's husband, George. He is brazenly dismissive of George and tells Nick that George is "so dumb he doesn't know he's alive." Humiliating George in front of his wife and in front of Nick is another way in which Tom likes to show off his supposed masculinity.