A Bad Boss can push your buttons like nobody else. Especially if you’re laboring under the tyranny of an Incompetent Boss, you may find yourself sputtering “But we already tried that” or “But that isn’t our department’s business” or “But that’s irrational!” none of which will get you anywhere. Except maybe in hotter water than you’re already in with said Boss.
An Incompetent Boss is just that--incompetent. Expecting anything sane to come out of his or her mouth is, simply put, delusional.
Instead, try to get something somewhat reasonable out of your Bad Boss by being what Mark Goulston calls a "plusser."
According to Goulston, "A plusser is someone who listens to what the other person says and then builds on it. One way of plussing is to use the phrase, 'Say more about ______.' Think of the words they [your Boss] used that had the most emphasis [or that you thought were the most sane] and invite them to say more about that topic. You will buy yourself time to think and calm down . . ."
Most importantly, you can reframe what your Boss said, in a new context that has some rationality to it, or some workability to it.
My preference, BTW, is rather than use Goulston’s "Say more about ______" is to say something like "Wow, that sounds really interesting. Would you tell me more about ________, please."