You can’t get away with saying, “That’s never happened. I’ve never disagreed with my boss.” Everybody, at some point, has disagreed with a decision the boss made about something. The question - behind - the - question is, how did you handle it? In this case, they’re looking to see that you have good communication skills and an understanding of authority. Can you get a competing idea communicated effectively and respectfully (without being rude or obnoxious)? Can you handle conflict in a professional manner?
You can tell your boss that you disagree about the way something should be, if at the same time you offer suggestions about how something should be handled. I personally think that’s always the best way: when you disagree, offer an alternative solution. Don’t just complain. But if the boss responds by saying, “I appreciate that, but we’re going to go in this direction,” then if you want to still continue to be employed, you’re going to have to give up. They’re the boss. (Unless for some reason, it’s incredibly unethical...but in most cases it comes down to a simple matter of ‘what the boss says, goes.’).
The story you tell should be an example of how you handle such a situation respectfully, professionally, and with good communication skills (just like if your boss disagrees with you ). This is a behavioral interview question, so use the STAR structure (Situation or Task, Action you took, Results you got) to tell your story. Just make sure that it’s a story that shines a nice light on you when you’re finished telling it. You don’t want to tell the story about the time when you disagreed but your boss was being a jerk and you just gave in to keep the peace. And you don’t want to tell the one where you realized you were wrong. Tell the one where your actions made a positive difference on the outcome of the situation -- whether it was a work - related outcome or a more effective and productive working relationship.
Here is a very general example:
“We were working on a big project for X, and my boss decided that we should take Y action. But I could see where that decision would cause us trouble down the road with A, B, and C. So I went to her, told her my concerns, and offered some alternative ideas [state what those were]. She saw my point and liked that I was thinking outside the box. We implemented my idea and it gave us X results.”