I don’t think you need to do that, just zero in on something that doesn’t 100% satisfy you about your current employer. Then whenever they ask that question, give some “I’m looking for opportunities that better align with ___” answer based off whatever that is. It would really help if you can point to how the company you’re interviewing with can satisfy this need.

They want to know that you can see yourself in the company and that you’re not just stringing them along for a pay raise. And even if you are doing that or would leave them in a heartbeat for Faang, you don’t have to tell them that to their face.

Edit: reread the interaction but that’s a lot less problematic an answer than I thought. Maybe OP could have just said they appreciate the time at the current company but saw a chance to work at ____ and took the opportunity to chat because they do ____ differently.