Just a light way to present some ideas about the Para Aduma.
As enigmatic as Para Aduma is reputed to be, many commentaries have attempted to explain the symbolism of many of the features of the Para Aduma. One of the most well-known ideas is that the Para Aduma is the metaphoric mother of the golden calf and is asked, so to speak, to clean up the mess made by her son.
The Para Aduma is treated as a kapara, an atonement, for the sin of the golden calf. Many details fit this idea nicely, but there is a problem. Para Aduma is not a korban. And being TAMEI is not a sin.
The potion of the ashes of the Para Aduma help rid a person of Tum'at Meit. No sin there. In fact, members of the Chevra Kadisha in all Jewish communities are highly praiseworthy. Big mitzva. No sin. Here is a possible way to connect the ritual defilement caused by contact with a dead body to sin.
The human body is the receptacle and partner of one's soul throughout one's lifetime. The person is commanded and challenged with Torah and mitzvot throughout.
A Jew is supposed to be a good partner to his/her soul, meaning, to live a Torah life. Sin basically goes against the person's Neshama. As a result, the body of the person after the soul departs is the major source of Tum'a. An eggshell and the peel of an orange serve a purpose during the time each is together with its contents. When the egg or orange is removed, the shell and peel have done their jobs and no longer have a purpose – but they are not defiled or defiling. A human body would not be either, one can suggest, if it were not for sin.
Therefore, that which purifies is, in some way, an atonement for sin. Para Aduma is presented to us with the well-known introduction: ZOT CHUKAT HATORAH. In fact, other mitzvot are also designated as CHUKIM in the Torah, and still more are CHUKIM (enigmatic mitzvot that we do because they are G-d's command, and not for reasons and rationales – as one can suggest about other mitzvot.
Rashi teaches us that the introductory statement about Para Aduma (and other CHUKIM) is our response to the scoffers of the world (non-Jewish and Jewish) and even our answer to our own evil inclination, the Yeizter HaRa. That response is: We do mitzvot because our King has commanded us – not because they make sense and appeal to our logic.
Some mitzvot do and some don't, But we do ALL mitzvot because G-d has commanded us. We must not feel like we are following things blindly. Our eyes are completely open to the concept of Torah, which is knowable up to a certain point, is the precious gift of life that G-d has given the Jewish people. Bottom line is that all mitzvot carry with them an element of CHOK. Even the most common sense mitzva has elements that defy our finite grasp. And even if there were a mitzva that made total, complete sense – we still should do it – first and foremost – because it is the command of G-d.