"They exchanged their honor for that of a cow eating grass". This is how Dovid HaMelech sums up Cheit HaEigel (Tehilim 106:20). Wouldn't it be more accurate to say that they exchanged His honor, rather than "their honor"? The Ralbag writes that G-d's honor is being referred to, but it is respectfully referenced euphemistically. Rav Nissan Alpert suggests a different approach which explains this reference to their exchanged honor. His approach also answers the question of why Chazal state that Parah Adumah is Kaparah for the Cheit Ha'Eigel. This in turn clarifies why it is appropriate to read Parshat Parah together with Parshat Ki Tissa, andthe story of the cheit ha’eigel.
The Jewish People at the time of the Cheit HaEigel were the Dor Deah - uniquely intelligent and sophisticated people. Thus, constructing the eigel must have been the subject of intense and profound debate . Rabbi Alpert suggests that the argument was as follows: The people who favored making the eigel wanted it to serve as a metaphor of the true nature of man, representing the fact that man is essentially an animal. They said that Moshe had lifted them up from their physical nature, but in his absence it was time to return to being what they really were - no different than a cow, eating to live and living to eat (this is implied by Shmot32:1 in which they refer to Moshe not simply as the one who took them out of Egypt, but as the man who raised them from Egypt - "Moshe, Ha'Ish Asher HE'ELITANU Mei'Eretz Mitzrayim.") Those who opposed the construction of the eigel felt strongly that man is primarily spiritual in nature and that it was therefore wrong to suggest the cow as a symbol of the essence of man. This explains why Dovid described the Cheit HaEigel as the time when Jews exchanged their honor for that of a cow eating grass.
There are various levels of tum'ah . The lowest level of ritual impurity, the avi avot hatumah, is a dead human being. The reason why the human corpse ranks lower than anything, including the carcass of an animal, is that a man's only real value rests in his soul. A dead cow can be utilized in many ways, but a dead man serves no real physical value. The Para Aduma comes to purify the lowest form of impurity - acquired through contact with a dead human being, and acceptance of these laws is reflective of an understanding that man's essence is his soul. This is why Chazal tell us that the Para Aduma is kapara for the Cheit HaEigel, the biggest mistake the Jewish People ever made. This is why we read Parshat Parah along with Parshat Ki Tissa.
May G-d help us all to remember - in the most painless way possible - that our essence is our souls.