In the Hebrew Scriptures, death was "dirty." For example, contact with anything dead (whether animal or man) made the Israelite unclean in the ritual sense. Thus any scavenger was not appropriate for human consumption, since such animals consumed the refuse and/or carcasses of other animals. Only animals who chewed the cud (and split the hoof) were consumed for food, since they were vegetarians that consumed living grasses and plants (which included certain fowl and insects as well). Likewise, fish with scales and fins were consumed, because their principal diet consisted of consuming what was alive.
What cleaned away death in the ritual sense was water, which was not contaminated by things dead. For example -
Leviticus 11:35-37 (NASB)
35 Everything, moreover, on which part of their carcass may fall becomes unclean; an oven or a stove shall be smashed; they are unclean and shall continue as unclean to you. 36 Nevertheless a spring or a cistern collecting water shall be clean, though the one who touches their carcass shall be unclean. 37 If a part of their carcass falls on any seed for sowing which is to be sown, it is clean.
The running water of the spring, or cistern collecting water, is unending and continuing and therefore cannot become "dirty." (The water is eternal, because it is unending and continuing.) In the Hebrew Bible it was such water that was filtered through the ashes of the red heifer that was used to "wash away" the dirtiness of those who were ritually contaminated by things dead (Numbers 19:1-22).
In the Christian New Testament these guidelines of ritual impurity do not apply, since cleanliness with eternal life occurs from within. (External ritual impurity from without therefore is moot.) That is, the Christian receives eternal life, and this water (unending, and continuing eternal life) cleans away spiritual death, which was what was "dirty." Like the unending water of the spring or cistern (eternal source), anything dead on the outside becomes moot. Thus the Christian may enjoy all foods with an open and clean conscience before God, although such liberty may cause Jewish Christians to stumble, and therefore should be avoided (Acts 21:25-26).
This imagery of death-impurity cleansed by continuous-water transitions from the Hebrew Bible into the Christian New Testament as "living water" or eternal life that takes away spiritual death, which is what makes the man "dirty" (what is on the inside versus what is on the outside).