Asking a duck to bark: 1. Requesting something impossible. 2. Deliberately requesting something impossible in order to humiliate a subordinate, preferably in public; blindly refusing to accept that something cannot be done. (see Bark into the wind, up the wrong tree; Impossible, nothing is)
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Herring, chasing a different: 1. Pursuing a fish of a different kind. 2. Aquatic analogy gone AWOL; loose grasp of piscatorial basics; extraordinary ability to distinguish between two different types of soft-finned teleost fish – a skill beyond most of us. (see AWOL, go; Bark into the wind, up the wrong tree; Fish up a tree, he looks like a; Sprat to catch a mackerel)