That is certainly an interesting question about rats and mice. Probably rats have a worse reputation in the West dating back to the Bubonic Plague, or Black Death in the middle ages (1300s). It was not the rats themselves, but the fleas that lived on the rat's hairy bodies that killed 1/3 of all Europeans.
Mice are always smaller, and don't seem as threatening as rats.
In defense of rats, some people in the rest have rats for pets, which they keep in a cage. There are not wild rats, but are bred for the purpose of being sold as pets, and are clean and healthy.
Maybe rats and mice do have a bad reputation in the West, but probably the Year of the Pig would be more disturbing to Muslims.
Personally, I don't think Westerners pay any attention to the significance of the rat as being the name of a year in China. They would just consider it an ancient astrological tradition and do not think that Chinese people would have any great affection for rats themselves.
There are many people in the West who are also interested in the Zodiac and astrology, and would be more interested in it from that consideration. Western astrology has a zodiac sign of "Cancer" which does not sound too inviting either.
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