Interestingly, the correct word for the hors d'oeuvres is antipasto. It is Italian from anti- (from Latin ante-) plus food (from Latin "pastus"). I got that from www.merrian-webster.com
I, like some other posters, was thinking it was supposed to be "ante" (like in "antebellum").
So Dogbert didn't have to mispronounce the word in order to pull Dilbert's chain.
Anti- can also mean "another" as it comes from the Greek (meaning something similar to "across" in the sense of "adjacent"). One derivation is "opponents" (which is the way SA is using it - thereby they "cancel each other out").
But if one wants to over-analyse (as most comments seem to do) then one could also say that "the man" would not be hungry, but tautologically sated.
Antipasto could only cancel out pasto. Pasta would be canceled out by antipasta. Thus, if a man ate pasta and antipasto, they would not cancel out, unless pasto or antipasta was also ingested. :)