Many of the unclean animals were, in fact, carriers of diseases, and would have been known to be so in the ancient world, which was much more sophisticated in such matters than modern folk may think. The pig, as you know, is more likely to be a carrier of disease than a cow. The birds which are unclean are mainly birds of prey, scavenging birds which ate carrion and more unhealthy for that reason. But this explanation likewise leaves much unexplained. For example, chewing the cud reminds one of contemplative meditation upon God's law.
Sheep remind one of the shepherd.
Pigs, on the other hand, suggest nothing positive. This explanation, however, leaves much more unexplained than it can account for. Finally, there is a new interpretation gaining ground among biblical scholars. We might describe it as the 'sociological explanation' for the distinction between clean and unclean animals. It has been advanced most successfully by a British sociologist by the name of Douglas in several books published in the 1960s and 70s.