To express that a false analogy has been made, people often say, “You’re comparing apples and oranges.” But are apples and oranges so different? After all, both are fruit; both are round; both grow on trees; both have lots of vitamins; and the similarities go on and on…
In order to truly convey the incomparability of two items, we should probably say something like, “You’re comparing chinchillas and Vikings.” Those two are much harder to compare… One is a rabbit-sized rodent indigenous to South America; the other is a plundering Swede from the 11th century.
Basically, almost any two random things would be better suited for this expression than “apples and oranges.” Here are 3 other possibilities:
1) …donkeys and Wite-Out.”
2) …negative amortization loans and chile relleno.”
3) …Charo and drip irrigation.”
***Please add more to the comments.***