The phrase "old fable" refers to a traditional story that is not true but teaches an important lesson or moral. It is a metaphorical term used to describe a widely known story that has been passed down through generations. Full definition
You have nothing but 2000 year old fables passed down by goat herders. (religion.blogs.cnn.com)
After 2,000 years of re-hashing these tired old fables and myths, not a single one has any shred of scientific evidence whatsoever to back them up! (religion.blogs.cnn.com)