I have come across the expression "That dog won't fly" (and you also find "This dog won't fly") in conversation and in the press. I have done a search on Google and the set expression (both versions) throws up 8 entries for each, which is remarkably little. I checked this website where odd metaphors are discussed, but it is not particularly illuminating on the expression itself. You just can't mangle a metaphor by accident. That dog won't fly. http://www.novelmatters.com/2010/07/assault-and-battery-of-metaphors.html The expression refers to a scheme, or idea, or project, or business proposal (etc.) that has been put forward and is deemed a non-starter, i.e. something that is doomed and will inevitably fail. It means, as I understand, in effect: Your idea is not going to work. Give up. I do not think the meaning of the set phrase can be inferred from the words, so it qualifies as an idiom or idiomatic expression: dogs are not known to fly. I am a bit puzzled by the expression and wonder what its origin is. Any link to the set phrase: And pigs will fly - used to comment on something someone says that is blatantly totally unrealistic? (E.g.: So, you're saying you will be earning £150,000 by the end of the year! And pigs will fly.) Insight welcome.