Rashi brings the Chazal that says that Parah Adumah is an enigma and the reason for the mitzvah is not public knowledge. Yet Rashi also says that the reason why the ashes of a Parah Adumah is used to purify contact with a deceased person is let the mother come (Parah Adumah) and cleanse the sin of the calf (referring to the Aigel). The second Rashi sounds like there is a reason for Parah Adumah. If so why is it called a chok which describes a mitzvah that has no logical explanation?

Let us first examine what it means when Chazal explain let the mother come and clean up the calf’s dirtiness. The chait of the Aigel came about because of Yisrael’s lack of emunah. when Moshe Rabbeinu did not appear after the designated forty days on Har Sinai the immediate reaction of Yisrael was to make an Aigel to replace Moshe. If they would have had strong emunah in Hashem and Moshe then we would have waited a little longer before reacting with the making of the Aigel. However the truth was that we lacked the necessary emunah. The Tikkun is therefore to require the emunah. This is accomplished by Parah Adumah which makes no logical sense and for this reason, it is called a chok.

So both Rashi’s are correct. Parah Adumah is beyond reason. Nevertheless, the reason is that the mother should come and cleanse her son. The cleansing is in order to get back to the lost emunah. In reality, it still remains a chok.