Even Prime Fallacy

The simplest possible Even Prime Fallacy is shown below:
Salviati: Most prime numbers are odd.
Simplicio: Two is even! Your argument completely falls apart.
We may express this idea more formally:
Salviati: p is sometimes true.
Simplicio: Yes, but p is sometimes false! Your argument completely falls apart.
Simplicio has failed to disprove Salviati, not because Simplicio's rebuttal is illogical or irrelevant, but because it is literally the exact same argument as the one Salviati made! "p is sometimes false" is an inevitable logical consequence of "p is sometimes true."
Someone who invokes an even prime fallacy probably thinks of an argument as "words you say in response to words someone else says," rather than as an exercise in logic.