If the preference order were (1. Barking Cat, 2. Barking Dog, 3. Meowing Cat, 4. No Pet)

That's strictly ruled out by the wording in the quote. While people often miscommunicate their preferences, I don't see particular evidence of it there, or even that the hypothetical person is under a misapprehension.

To take it back to metaphor: the flip side of wishful thinking is the sour grapes fallacy, and while the quote doesn't explicitly commit it, without context it's close enough to put me moderately on guard.