Chinese Festival stories

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I'm currently learning Mandarin Chinese and about a couple of weeks or so ago we learned about the Moon festival where people reunite with their elderly and eat homemade food as well as eat moon cakes. It's similarly interchangeable with America's Thanksgiving, but mainly gives off the difference in its date. The main thing I want to know is how the stories of a Jade rabbit as well as Chang 'e and Houyi (a female goddess and a male immortal respectively) had these stories? It seems too out-of-hand, and I'm in complete disbelief that it's the reason why people celebrate the moon cake. Perhaps I'm too majorly influenced by Western culture, but regardless, it's really something different that I didn't expect.