The detail from "The Mystery of the Missing Hamburger" that best explains why Juan believes that Vinnie would not have wanted to eat Veronica's hamburger is:
Veronica likes plain hamburgers while Vinnie likes burgers with pickles, cheese, and ketchup. Also, Vinnie has a half-eaten hamburger on his plate.
"He reached down and picked up a plate from the floor next to him. A half-eaten burger sat on it. He signed again. Veronica translated.
'He says he'd never eat one of my plain, dry, boring burgers. He thinks a breakfast burger needs ketchup, cheese, and pickles. Like this.'"
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