Chewing cud or rumination is the act of regurgitating bolus or semi-digested food (cud) back into the mouth from the rumen for further mastication. In English, the phrase can mean to reflect over something.
Usually, when ruminant eat food, they do it rapidly and it goes to their rumen (the first part of their four stomach chambers) where it mixes with some digestive fluids, some microorganism and some digestion occurs. The food becomes softer and bolus.
While resting, these animals will regurgitate the food back into the mouth for further mastication before they can swallow it again. This is what rumination is all about.
Several animals are known to ruminate. They include cows, goats, sheep, camels, chevrotains, buffalos, the deer, alpacas, giraffe, antelopes, moose, elk, bison and so on.
Most of these animals are hoofed mammals. What about hares and rabbits?
Do rabbits chew their own cud?
If you study the digestive system of rabbits, you will realize unlike ruminants, they are hindgut fermenters, i.e., their fermentation occurs in the cecum. Furthermore, you should know that rabbits cannot vomit or even burp, a reason why they often suffer from hairballs and gas quite often.
From these facts, you should already be aware of the fact that rabbits do not chew cud. How else would they regurgitate food back into their mouth if they are unable to even vomit in the first place?
Finally, bunnies are not even ruminants. They are lagomorphs and lagomorphs are not known to chew cud since they have only one stomach chamber and not four like ruminants do.
Perhaps what brings the confusion is the biblical reference. The Bible mentions hares to be cud chewers. However, in actual sense, they are not. They only participate in cecotrophy or coprophagy where they eat their cecotropes.
Since the Bible was written in Hebrew, perhaps, it could have meant something else and it could have been used to refer to cecotrophy or something of the sort.