And he took [the gold] from their hands, and he fashioned it with a graving tool, and made it a molten calf (32:4)
Aharon's report perfectly parallels this pasuk, but with each phrase restated to clear himself of active involvement:
וַיִּתְּנוּ-לִי; וָאַשְׁלִכֵהוּ בָאֵשׁ, וַיֵּצֵא הָעֵגֶל הַזֶּה.
And they gave it to me, and I tossed into the fire, and out came this calf (32:24)
Chumash's narrator paints Aharon an active party: taking, fashioning with tools, making the calf. Aharon, however, prefers a thoroughly passive model: they gave, he merely tossed, out came this calf.
While it is certainly uncomfortable to point out flaws in beloved Biblical characters, Chumash offers several other signs that Aharon indeed sinned. Moshe begins and ends his conversation with Aharon with tones of blame: “What did the people do to you, that you brought upon them a great sin!” (32:21) is followed by the damning conclusion, “for Aharon let them loose for a derision among their enemies.” (32:25) Indeed, the last verse of the perek says it all: “and God struck the people, on their making the calf - which Aharon had made.” (32:35)
The question thus becomes, how did Aharon react to this? How did our Biblical hero respond to mistakes? Parshat Shmini describes a special sin offering, an “eigel ben bakar” (a calf, Vayikra 9:2), brought by Aharon during the Mishkan’s dedication. It is the only mention in Tanakh of a calf brought as Korban Hatat and it is plausible that Aharon is addressing this very point – he is recognizing and doing Teshuva for his role in Egel haZahav. Before assuming his position as Cohen Gadol, he repents and admits his previous misstep.
But one perek later, a more tragic example emerges. Aharon's two sons, Nadav and Avihu bring a foreign flame into the Mishkan, and in response . . .
וַתֵּצֵא אֵשׁ מִלִּפְנֵי יְהוָה.
And a flame went out before God and devoured them (Vayikra 10:2)
The unique phraseology is eerily similar to Aharon’s questionable conversation with Moshe:
וָאַשְׁלִכֵהוּ
בָאֵשׁ, וַיֵּצֵא הָעֵגֶל הַזֶּה
And I cast it into the flames, and out came this calf (32:23)
This textual link may point to yet another moment of the healing process: Aharon creates a god from flames, his beloved creations are destroyed in Godly flame. (This is not to claim that Aharon's sons suffer the sins of their father, but that their deserved death occurs in a highly symbolic manner - one which Aharon likely did not overlook.) This tragic moment, the low point of Aharon's life, is also his most crowning act of Tshuva.
For a key aspect of Aharon's previous misdeeds was his failure to admit any guilt. He responded with excuses, expending a full three pasukim to attack Bnei Yisrael while distancing himself from his own crimes. Bearing this initial reaction in mind adds to the power and depth of Aharon's response to his sons' death:
וַיִּדֹּם אַהֲרֹן
And Aharon was silent (10:3)
Viewed through this light, Aharon's quiet is not (only) the pious acceptance of God's will, but the humble recognition of his faults, his guilts, and the arduous path that is transformation from sinner to Cohen Gadol.