Why do Daisy and Tom Buchanan invite Nick to dinner?
At the beginning of the novel, Nick Carraway moves from the Midwest to New York to work in the bond business and rents a home in the West Egg section of Long Island. Upon arriving in New York, Nick is not acquainted with anyone and only knows his second cousin once removed, Daisy, and her husband, Tom Buchanan, who live in the aristocratic East Egg. Daisy and Tom initially invite Nick over to their home as a nice gesture and an opportunity to introduce him to Jordan Baker, who is a professional golfer and attractive single woman. Daisy is friends with Jordan Baker and plans on hooking her up with Nick, and Tom views Nick's visit as an opportunity to brag about his estate. During Nick's visit to their home, he becomes aware of Daisy and Tom's marital issues, particularly Tom's infidelity. Nick also finds Jordan Baker attractive and goes on to date her over the course of the summer. Later on, it is revealed that Daisy used to have a relationship with Nick's enigmatic neighbor, Jay Gatsby, and Nick serves as the intermediary between the both of them.
Nick is newly home from the war. He is a first cousin to Daisy and Tom is her husband. They invite him to Tea and Jordan is there. They invite him because he is family, he is single, they have a single female at the house and the "custom" was to "fix up" the single woman with an appropriate man. Also, Tom is intent on having a bragging session with Nick present. He pontificates on the difference between East Egg and West Egg and he flaunts his affair with Myrtle Wilson while Jordan, Nick and Daisy are at the dinner table. This is Nick's introduction to Tom, his cousin's husband.
Nick is Daisy's second cousin and Nick had known Tom in college. Daisy lived in Louisville, the same town Nick was from until she married Tom and they moved to the East coast. In fact, when Nick first sees Daisy again, she asks playfully , "Do they the people of Louisville) miss me? Nick answers, "The whole town is desolate. All the cars have the left rear wheel painted black..." Daisy retorts, "How gorgeous! Let's go back, Tom. Tomorrow!" Of course, Tom and Daisy will never go back to the Midwest because they have throughly accustomed themselves to the East Coast and its values.