In The Great Gatsby, why does Tom insist on switching cars with Gatsby when going to town?
What a loaded question! There can be numerous topical answers, but only one answer that reads between the lines: Tom switches cars with Gatsby so that George and Myrtle Wilson can get a good look at the yellow car that eventually becomes "the death car," thus cementing the end of the novel.
Let's deal with the topical answers first. Keep in mind that one can speculate, but no one knows the "real" answer here. One idea is that Gatsby has just suggested taking everyone in his car, and Tom wasn't going to be caught dead agreeing with the man who has his eyes on Daisy, so Tom suggests a different idea. Tom is hoping to remain in control (as he always is). The second idea is a bit more psychologically complex. Tom has just discovered that his wife has swapped him for another lover (Gatsby). In a insidious bit of sarcasm, Tom almost asks, "Why not swap cars, too?" Of course, Tom planned to take Daisy along with him, . . . on Gatsby's turf (in his car), but Daisy has other ideas. She immediately insists on riding with Gatsby on Tom's turf (in Tom's car). This shocks Tom, as Gatsby now rides off with Tom's girl in Tom's own car. His original bout of sarcasm has backfired. I suppose that my last idea is a bit more crude: Tom is making a metaphorical comment giving him the upper hand, "Hey, if you're going to ride my pretty wife, I'm going to drive your swank car!" And in his hatred and disgust suggests an even swap.
Now for the "real" answer. Fitzgerald needs Tom to take Gatsby's car in order for the plot to continue toward its climax. George and Myrtle Wilson get a really good look at Gatsby's yellow car when Tom stops for gas. This is the same car that will kill Myrtle in a very short time. At this point both George and Myrtle think the yellow car belongs to Tom. This is the reason why Myrtle comes running desperately out to flag it down later (because she, of course, supposes Tom would still be driving). This is also the reason why George, in a desperate rage, eventually corners Tom as to the rightful owner of that car. Then the murder/suicide of George Wilson and Gatsby ensues.