The Book of Leviticus contains some dietary laws for the Israelites. In particular, animals that both chew the cud and have divided hoofs can be eaten, but not animals that fail either of these requirements. This is Leviticus 11:3-6:
Deuteronomy 14:7 is the same. Note that the word "hare" is sometimes translated as "rabbit" instead. In either case, it's not correct to say that they chew the cud. Rather, they practice "coprophagy" - that is, they eat some of their own droppings for additional nutrients. By contrast, animals which "chew the cud" (such as cows) have complex digestive systems in which partially digested food is returned to the mouth for further chewing. These animals are called "ruminants".
The question really is whether our English Bible translations are accurate, and also whether the term "chewing the cud" could have a less technical meaning, which might include rabbits or hares. Certainly it's unreasonable to expect the language and idioms of ancient Hebrew to correspond neatly to our modern terms. Perhaps for them the phrase could include rabbits and hares.
Only a deep and technical examination of the ancient Hebrew could really decide the issue.
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