If we had a recipe for pie, there's a few things we might expect. If we doubled the ingredients, we'd probably get double the pie. But if we took the ingredients and cooked them separately, we wouldn't expect to put them together and get our pie back. You can't bake the eggs, flour, and sugar in separate ovens and plop them together at the end.
This is a companion discussion topic for the original entry at https://betterexplained.com/articles/analogy-math-and-cooking/