Why do Daisy and Tom Buchanan invite Nick to dinner?
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.