To be in a difficult situation is like hanging "on" a "hook"; to get free of the problem you must get "off the hook". Example: "We've caught you again, but this time you won't get off the hook so easily!" You are "off the hook" when you are no longer responsible for some problematic situation. Example: "We found the guy who stole the money, so we know you didn't do it; you're off the hook." When you get yourself free from a difficult situation you are no longer "on the hook"; you are "off the hook." Example: "You're lucky; it turns out that Dad never heard you come in late last night." Answer: "Great, that means I'm off the hook!"