This is a somewhat puzzling assertion – it is unclear where exactly in the Torah we find such a commandment (See Magen Avraham, O.C. 685, and Arukh HaShulchan 685:7). Such a gaping hole has led some authorities (such as the Vilna Gaon) to maintain that the entire reference is actually a scribal error, and the reference was not to Parashat Parah but another section referred to with the same initials such as the aforementioned passage about Amalek, or “Parashat Purim”. Others, hesitant to label as error a statement found in numerous rishonim, offer innovative theories to explain the source. (See, for example, Meshekh Chokhmah and Torat Moshe, as well as Responsa Divrei Yatziv, Orach Chaim 288).
One theory that is put forward (see Artzot haChaim of the Malbim, Hilkhot Tzitzit, and Responsa Arugat HaBosem, Orach Chaim 205) concerns those select concepts and commandments that the Torah has distinguished with an imperative of “remember” (the zekhirot). Authorities differ as to the precise count of these precepts, but they include prominently such concepts as Amalek, Shabbat, and the exodus from Egypt. And indeed these three find halakhic expression: we remember Amalek through the special k'riat haTorah; Shabbat through kiddush Friday night; and the exodus in mentioned twice a day in the third paragraph of k'riat shema.
However, one concept that appears to deserve inclusion seems to lack halakhic representation. The Torah commands: “Remember, do not forget, how you angered Hashem, your G-d, in the desert.” (Devarim 9:7). If so, how come no ritual or reading commemorates the incident of the golden calf? Should there not be an implementation in Jewish practice of this obligation?
Therefore, it is suggested, that perhaps this could indicate a source for a biblical obligation of Parashas Parah. Chazal perceived a linkage between the mitzvah of Parah Adumah and the sin of the golden calf. As Rashi quotes, “Let the mother come and clean up the soiling of the child”. The adult cow symbolizes the parent, and in atoning for the sin is “cleaning up” the mess of the calf.
Within that understanding, it may be posited that the sin of the calf is indeed commemorated, in an indirect manner. Rather than directly evoke the disgraceful episode of the golden calf, we chose a less embarrassing path, reading of the commandment that atones and not the transgression that incurred guilt.
Such a reading would reflect back on the very nature of the obligation of remembering the calf. The focus is not on the sin, but rather on the path back from impurity. The Torah wishes to impress upon the psyche that even in the aftermath of egregious moral failing the route of return remains open.
However, there were those who assumed a different theme in this commandment of remembering. Some suggest that we are told to constantly recall the instance of the calf as a cautionary measure. At the time of the sin, the Jewish people were on an extremely high level of spirituality, so close to the occasion of the giving if the Torah. At such a time, one may believe himself invulnerable to temptation or moral error, protected by a bubble of holiness. The incident of the calf must always be remembered to warn that no one is protected in that manner, and that descent to sin can happen whenever inadequate care is taken.
If that is the theme, then, it would seem that using the Parah Adumah as a reminder would be an ineffective method. It may represent atonement, perhaps, but the message of spiritual vigilance would be lacking.
However, it might be suggested that even this motif is present as well in the Parah Adumah. We are well aware of the central paradox of this commandment. At the same moment that it confers purity upon the impure, it incurs impurity on to the purifiers. From a straight logical perspective, this is confounding: is the Red Heifer a vehicle of purity, or of impurity?
It might be suggested that this is precisely where the warning of Parah Adumah lies. At times, one may feel on such a high level as to be invulnerable from stumbling. This could have been the mentality of the Jews at the time of the golden calf; at such a point in history, how could they sin? We are bidden to constantly remember this incident in order to remind us that no one is absolved of the responsibility of personal vigilance.
In its own way, the Parah Adumah makes this point as well. If one is involved in a religious activity, in a rite of purification, it might be assumed that one is insulated from any spiritual failing. Yet, we find that even this activity contains the elements of impurity. The message is clear: no context or activity is a spiritual guarantee; it is only through constant, careful, self-awareness that one can ensure that his behavior is actually a true expression of the ratzon Hashem.