Well, as Scott Adams says, "Analogies are for fighting."
If an analogy is supposed to persuade me, but the internal premise of the analogy completely contradicts the purpose of the analogy, then perhaps it should be completely eliminated or at the very least it should be challenged.
Moreover, this contradiction within the analogy highlights the exact opposite. Likely, the CEO of Coca Cola experiences that "coke/pepsi" dialog with waiters all the time and merely shrugs it off --- because that is actually a reasonable response, unlike screaming at people over a tiny, unintentional slight.
For any decently structured argument, analogies are illustrative, not load-bearing. If you find that is not the case, usually the argument is not particularly sound.