'Wrongheaded' (also written 'wrong-headed') describes an idea, plan, opinion or decision that is not just mistaken, but mistaken in a stubborn way — the person holding it will not look again, will not listen, and keeps pushing in a direction that will not work. The 'head' in it is the person's thinking. Their head is pointed the wrong way. So the word carries a judgement about the thinker as well as the thought: 'a wrongheaded policy' says the plan is bad AND that the people behind it should have known better. That is why it is a favourite in newspaper opinion columns, book reviews and political argument — it is a polite-sounding word that is actually quite sharp. We use it mostly for ideas, approaches, policies, attempts and beliefs, and sometimes for the person: 'he is wrongheaded about this'. It is not for simple factual errors. If someone says Taipei is in Japan, that is just wrong, not wrongheaded. Save 'wrongheaded' for a whole way of thinking about a problem that you believe is aimed in the wrong direction. It sounds formal and educated. In casual talk people say 'that's the wrong way to think about it' or 'he's got it backwards'.

想法偏差的、執迷不悟的、方向就搞錯了的（不只是錯，還帶著固執、不肯改的意味；常用在批評政策或主張）