Do you think the CEO of Coca-Cola actually screams at waiters when they say, "we don't have Coke, will Pepsi be ok?"
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.