Not rude at all.
However, I can see how he would have interpreted your replies as rude. In fact, I don't know how you can re-read that exchange and not realize it. Sometimes it takes a fresh perspective and third set of eyes to see this. Maybe you didn't intend for it to be that way, but it sure came off that way. People in customer service positions are there for customer service, but they're not your vassals or anything.