The two features stated in this pasuk are signs which identify permitted animals. No reason is stated as a rationale for their permissibility. The Abarbanel suggests that animals which chew their cud are not capable of crushing and chewing up bones. Consequently, they feed on plants, and they do not have the ferocity of wild animals. Their split hooves do not have claws, suggesting that these are peaceloving and relatively harmless animals. Indeed, these animals reflect the traits of compassion and mercy, which are the hallmarks of the Jewish personality.
In a similar sense, Rabbi S.R. Hirsch z.l. explains that two instinctual acts are essential to the life of an animal: the search for food and the struggle for survival. Indeed, these two activities are indispensable to human life. For the Jew, however, although they are essential, they must be subordinated a more sublime goal. Those animals whose distinct features and organs reflect these two functions (the claws of the wild animals and the stomach that quickly and indiscriminately digests all swallowed food) are excluded from consumption by the Torah.
Hooved animals and those that chew their cud exhibit a form of “refinement,” which is integral to the Jewish character. Thus, these two prerequisites for kashrus contribute to the development and perpetuation of Klal Yisrael’s dignity and distinctiveness.