I once went to dinner with a fellow American who had just arrived in Tokyo for a conference on his first visit to Japan. He wanted an authentic Japanese meal, up to a certain price range, so I arranged dinner at a fairly pricey place that served a reasonable approximation of a kaiseki meal. (I knew about it because some Japanese friends had taken me there.)
As we settled in, I explained what the menu options were and what the food items consisted of, so he made his choice of the A, B, or C course. Then he topped it off by telling me (and he had a loud voice that could be heard over the rush hour crowd at Shinjuku), "And I like a glass of milk with that."
The waitress had obviously understood his request, because her jaw dropped open.
I told him that I would be very surprised if they even had milk on the premises.
"Well, why not? They should!"
"Because you wanted a traditional Japanese meal and that does not include any dairy products." I had to break the news to him that if he wanted milk, he'd have to buy it separately at a convenience store and drink it between meals, because few if any restaurants were likely to have it on hand. I neglected to mention that the thought of drinking milk with traditional Japanese cuisine was downright nauseating to me.