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Very good explanations so far!

I can add one, which is shocking not only for the foreigners, but also for a lot of Chinese abroad and Chinese in China. The dish named 'Phoenix, Dragon and Tiger' (or something like this, I'm not sure about the order of the words). Now take a deep breath and see it: phoenix = chicken, dragon = snake, tiger = cat.  A simpler version: only cat and snake (龙虎斗): http://baike.baidu.com/link?url=AqPzspQR-1VGl83ghCfZ0d_9zscu2xPFygjvMsrnK8wVhYfRfW5VSmZvqnC5wmhWtN4D7xshZO0jZ-VvmYj7tGmK9dc9Cy8tGYFYZtP6Sri

These dishes are pretty local ones and I never ate them, nor people around me and people I know (as far as I know). So, it's much more exotic than common. Once I watched a film about baked rats restaurant in the USA. And I was sure it's something very local. I'm not sure in which state it was. All I found now is about some 'rat stew': "Rat stew is consumed in American cuisine in the state of West Virginia..." (https://en.wikipedia.org/wiki/Rat#As_food).