In ancient times, anyone who wanted to be on the Temple Mount had to go through a process of preparation that involved immersing in water into which the ashes of a red cow had been dissolved. The terms used are ‘pure’ and ‘impure’ but these had nothing at all to do with cleanliness. They merely marked the difference in states, like say, having a pass to get into the White House. It is like food we can eat and food we can’t. The same terms, pure and impure are used but they do not mean for example that a cow is any cleaner than a horse or a camel. Just that some animals we may eat, and others not. It’s a ritual thing, not a scientific thing. Indeed, the priest who prepared and the priest who burnt the sacrificed animal to dissolve them into water, became impure themselves which is counter intuitive.
This is why the Torah applies the term Hok. Meaning a non-rational and non-utilitarian law. You might say an act of faith. Still, it all sounds very strange that they should use a red cow. A similar law involves a cow being slaughtered in the ritual of exculpation when a dead body was found with no clue as to how or why. The elders of the nearest town had to bring an offering to symbolically purify themselves from guilt.
Calves, cows, bulls all played an important part in ancient Mesopotamian rituals. They were often deified too. After the Golden Calf episode in which the Children of Israel were seduced into idolatry, it was only when Moses ground the idol into dust and dissolved it into water and made everyone drink it that the impurity of the action was removed. The significance was that something one consumes cannot have any power and the cow, calf symbolized everything that was corrupt in pagan society. Even so the Israelites kept on worshiping Golden Calves.
But if the ashes purified, the priests who carried out the preparation became the opposite. How can the same thing represent pure and impure, good and bad? The fact is we humans are just like that. We are intrinsically neutral but we can use ourselves, develop ourselves well or badly. We have the capacity to make something holy and good out of ourselves or profane and sinful. We contain the means of both.