The Zodiac Curse.

From the anime Fruits Basket.

Once upon a time, God invited all the animals to a banquet for a party and everyone of the animals were invited. That day, the rat decided to play a trick on the cat and told him it was the day after.
Then, the rat rode on the cow's back followed with the rest of the animals except for the cat who was asleep at home, happily waiting for the banquet that would never come.

the Soma Family was a Family who had been cursed down to genreations to take the form of the chinese zodiac animals when they are hugged by someone the opposite sex ( besides from the people who share the same curse.) or get too overwhelmed. It has been under them for generations and generations, if anyone from the outside had ever found out about their curse, their memories will be erased by their inside doctor, who is also cursed with one of the animals from the zodiac.
The cat as well is cursed, even though some are not sure why since the cat is not accepted into the family as well as the zodiac time. Nonetheless, it is cursed, just not accepted.
As the story goes, the cat and the mouse are still enemies to each other. as the story takes place, the feelings of all the animals towards each other are all the same.