Am I weird?

You see, I'm front of house staff in a museum. I meet and greet people all day long and I NEVER ever say 'have a nice day' when they leave because I feel it's such a cliche and nobody British believes that you mean it. Instead I say things like "I hope the weather clears up for you' or 'remember, it's LEFT at the traffic lights because right takes you into the one way system and, believe me brother, you don't want to go there' or something else relevant to whatever we've been talking about. But lately I've had a few people who have very pointedly said 'have a nice day' to ME with the kind of slow patient cadence that suggests they are trying to teach me how it's pronounced.

Am I being incredibly bad mannered by not wishing people a nice day? Has that little phrase become such an accepted part of every public transaction that it's essential? Are overseas visitors going away thinking, "that woman answered all my questions and drew me a map to White Castle but she didn't wish me a nice day so OMG maybe she doesn't give a damn about me"? Am I ruining people's days by not hoping they have a nice one?

I'd better make it clear that I have NO plans to start trotting out that trite little phrase because I'm perverse like that, but I might just try to be a little bit nicer to them before they leave to make up for it.