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The Bible's definition of "chews the cud" is simply different from the technical definition we are thinking of. When the Bible says that the rabbit (or hare) and rock badger "chew the cud," it is simply saying that they make a chewing motion that looks like what other animals do when they "chew the cud." There is nothing wrong here because the Bible sometimes speaks generically and does not claim to be a technical or scientific textbook.
Some argue that the Bible is incorrect when it says that the rabbit/hare and rock badger "chew the cud," and so it cannot be infallible or inerrant. Here is the relevant passage:
Leviticus 11:5-6- 5 And the rock badger, because it chews the cud but does not part the hoof, is unclean to you. 6 And the hare, because it chews the cud but does not part the hoof, is unclean to you.
The Bible's definition of "chews the cud" is simply different from the technical definition we are thinking of. When the Bible says that the rabbit (or hare) and rock badger "chew the cud," it is simply saying that they make a chewing motion that looks like what other animals do when they "chew the cud." There is nothing wrong here because the Bible sometimes speaks generically and does not claim to be a technical or scientific textbook.
Here is what Norman Geisler says about this topic:
It is known that rabbits practice what is called "refection," in which indigestible vegetable matter contains certain bacteria and is passed as droppings and then eaten again. This process enables the rabbit to better digest it. This process is very similar to rumination, and it gives the impression of chewing the cud. So, the Hebrew phrase "chewing the cud" should not be taken in the modern technical sense, but in the ancient sense of a chewing motion that includes both rumination and refection in the modern sense.[1]
Some people have trouble accepting possible explanations to alleged contradictions in the Bible, especially ones that they consider a stretch. For example, Dan Barker, president of the Freedom From Religion Foundation, says this:
I have received numerous replies from Christians who think that these contradictions are either trivial or easily explained. Yet not a single "explanation" has been convincing.
The fact is that there are plausible explanations for every alleged contradiction in the Bible. That there is a plausible explanation for an alleged contradiction does not mean that it is definitely the correct explanation for the alleged contradiction.
However, as long as a possible explanation has been suggested, then it has been objectively demonstrated that there is no necessary contradiction regarding the Bible verses and passages brought up.
When people like Dan Barker say that they don't find a particular explanation for a contradiction "convincing," then that is merely their opinion. A plausible explanation has been suggested that eliminates the necessary alleged contradiction. They simply don't like it, which is not at all a relevant argument against the explanation.
To read more about solutions to Bible contradictions and difficulties, check out Norman Geisler's The Big Book of Bible Difficulties: Clear and Concise Answers from Genesis to Revelation. While we do not agree with some of Geisler's theology, particularly concerning his view of predestination, this book is still an excellent resource. It is thorough and filled with research.
Another book to check out is Tim Chaffey's Demolishing Supposed Bible Contradictions: Exploring Forty Alleged Contraditions, which also answers many alleged contradictions in the Bible.