Note that God began positively. He told the Israelites what they could eat ( Leviticus 11:2-3; cf. Genesis 1:29-30; Genesis 2:16-17). Then He gave them a list of unclean land animals ( Leviticus 11:4-8). [source][source][source]
Perhaps animals with cloven hoofs were unclean because they had only two digits instead of the basic five and were therefore thought of as abnormal. [1][source]
Apparently the technical definition of chewing the cud that we use today is not what the Hebrews understood by chewing the cud. Today we use this term to describe animals that do not initially chew their food thoroughly but swallow it and later regurgitate it and then chew it thoroughly. Some of the animals described in Leviticus as chewing the cud do not do that (e.g, camels [2], conies [3], and hares). However these animals do appear to chew their food thoroughly, so this may be what the Israelites thought of as chewing the cud. [source][source][source]
Any dead animal was unclean, perhaps because death was not the normal condition of an animal. [source][source][source]
"Sheep, goats, and oxen were the standard sacrificial animals of pastoralists. They have in common cloven hoofs and rumination. Interpreting this theologically one might say that as God had limited his "diet" to these animals, so must his people. It is man"s duty to imitate his creator ( Leviticus 11:44-45). When the Israelite restricted his food to God"s chosen animals, he recalled that he owed all his spiritual privileges to divine election. As God had chosen certain animals for sacrifice, so he had chosen one nation "out of all the peoples that are on the face of the earth" to be "a kingdom of priests and a holy nation" ( Deuteronomy 7:6; Exodus 19:6)." [4][source]