When explaining the principle underlying the Red Heifer, Rashi states that parties may taunt the Jews about the Torah and its reasoning, to which the response is simply that God decreed it; we have no right to challenge it. It is chok. This indicates that there is no true reason for the Red Heifer; it is a microcosm of our faith and trust in God.
But Rashi goes on to quote R’ Moshe HaDarshan that it atones for the sin the Golden Calf. Which is it?
The Bikurei Avraham and Kehilas Yitzchak teach that all explanations for the Red Heifer ultimately conclude that it atones for the Golden Calf; precisely because of the fact it has no essential reason.
The sin of the Golden Calf was that the Jews threw off the yoke of heaven and cast aside their duties. The equal and opposite would be to take on something unquestioningly. Thus, the explanations by Rashi operate together; we don’t really know the reason for the Red Heifer, which is precisely why it atones for Golden Calf.
The Panim Yafos notes that the Gemara in Brachos states that recalling a previous sin draws new attention to it, and it comes under scrutiny again in Heaven to some degree. This is potentially why parties inquire what the Red Heifer is for. Since it is because of the Golden Calf; we answer that it is an unknowable chok.
R’ Chaim of Alexander notes that the Torah says the word לֵאמֹר – “to say”, with regard to the Red Heifer, twice, because there are two things to say:
וַיְדַבֵּר הֹ אֶל מֹשֶׁה וְאֶל אַהֲרֹן לֵאמֹר – Hashem said to Moshe and Ahron to say…
זֹאת חֻקַּת הַתּוֹרָה אֲשֶׁר צִוָּה הֹ לֵאמֹר – These are the decrees of the Torah that Hashem commanded; to say…
It is not the same thing said each time, because there are two answers. If enemies and miscreants ask, its a chok. If R’ Moshe HaDarshan asks, then there is a great reason!