Why does Gatsby object to letting Tom drive his car in chapter 7 of The Great Gatbsy?
Gatsby does not want Tom to drive his car because he does not care for Tom, and he is in love with his wife.
After the lunch with Jordan, Daisy, Gatsby, Tom and Nick, a trip to town is proposed. When Tom suggests that he drive Gatsby’s car, Gatsby finds the suggestion “distasteful.” He suggested his car, but there is no reason for Tom to drive it.
Tom’s suggestion to drive the car is presumptuous. Gatsby does not approve of Tom, and the car is symbolic to Gatbsy. Throughout the novel, cars are flashy and luxurious. Gatsby’s has green leather! Such a status symbol did not belong in the hands of one such as Tom.
Most men do not want others to drive their car, because for a man a car is more than a vehicle. It is an outward representation of masculinity. Tom is tentative and drives the car jerkily. Tom is pretty incredulous about Gatsby, and it’s clear he does not like him. It’s only natural that Gatsby does not want him to drive his car. Tom disparages Gatsby’s car, calling it a “circus wagon.” Tom’s suspicions are warranted.
She had told him that she loved him, and Tom Buchanan saw. He was astounded. His mouth opened a little, and he looked at Gatsby, and then back at Daisy as if he had just recognized her as some one he knew a long time ago. (Ch. 7)
Tom’s reaction to Gatsby is to be expected. He is worried that his wife and Gatsby are too friendly, and he is trying to impugn Gatsby’s manhood by driving his car.
I am quoting the entire answer written by luannw, and I have also provided the link to it. This answer explains it very well.
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.