In chapter 7, why does Gatsby object to letting Tom drive his car?
In Chapter 7, it's a very hot summer day and Gatsby has been invited to lunch at the Buchanan's, along with Jordan and Nick. Tensions rise higher and higher in the heat, especially after Tom realizes that Daisy is in love with Gatsby. He is "astounded," but also determined to get control of the situation. When Daisy insists they all go to "town" (New York City), he angrily agrees. He and Gatsby then get into a covert battle over dominance—Gatsby suggests they go in his large yellow car. Tom instead says he himself will drive Gatsby's car, which is bigger and brighter than his own, while Gatsby will drive his coupe.
Nick tells us the idea is "distasteful" to Gatsby, and Gatsby objects that his car might not have much gas. Tom pooh-poohs that worry and, in fact, stops for gas at Wilson's gas station. He wins this first battle with Gatsby and does drive his car, establishing some dominance; however, it's not yet a complete victory as Daisy chooses to go with Gatsby in Tom's car.
The battle over who drives the car is a proxy battle over Daisy by two dominant males. Gatsby doesn't want to give in to Tom by letting him drive his car.
Gatsby is proud of his car because, like Gatsby's house and Gatsby himself, the car is ostentatious. In chapter 4, when Nick describes it, the reader discovers that it is, "a rich cream color, bright with nickel, swollen here and there in its monstrous length with triumphant hat-boxes and supper-boxes and tool-boxes, and terraced with a labyrinth of wind-shields that mirrored a dozen suns. Sitting down behind many layers of glass in a sort of green leather conservatory, ...". To Jay Gatsby, being wealthy meant showing off that wealth. He has the money to fit into Daisy's world, but he doesn't have, nor will he ever have, the class that would put him in Daisy's world. Daisy's and Tom's car is a much more sedate, refined navy blue. To those in the Buchanan's social strata, being wealthy was just a fact of life they'd always known and to be showy was distasteful and crass. It's a sad note throughout the story that Jay never grasped that difference. So, Jay would much prefer driving his own bright, shiny roadster with his bright, shiny Daisy beside him than to drive Tom's dark, sedate sedan.