Even after leaving Egypt, Bnai Yisrael were slaves. God redeemed them through midas ha-rachamim. (Ramban, Shemos 15:6 and 32:11). Midas ha-din requires human agency: man will receive what he works for. Midas ha-rachamim obviates the need for human agency: God will provide salvation, even if undeserved. Bnai Yisrael had no role in their own redemption; they were passive participants in their own history; they did not appreciate their own agency. Indeed, they did not have agency. Bnai Yisrael operated only with a sense of midas ha-rachamim: they were freed slaves, not free men.
Therefore, when Moshe left them for Sinai, they descended into crisis. Here they were, alone in a barren wasteland, without a leader. Self-governance requires self-confidence. Self-confidence requires competence. Bnai Yisrael preferred abdication of responsibility, which confers self-confidence. Bnai Yisrael wanted a leader to alleviate the burden of responsibility. It is much easier for a slave people once freed to depend on the masterclass than to rise to the stature of freedom.
The calf is a working animal: it pulls plows, wagons, and tills the soil. It therefore represents midas ha-din: The calf gets what it works for; if it does not till the soil, the soil will not be tilled. Aharon sought to impress upon the Jewish people that they could relieve their anxieties about their circumstances through their own efforts: they needed to incorporate midas ha-din into their worldview. Aharon sought to create a national symbol for Bnai Yisrael which would inspire accepting the yoke of responsibility. The calf meant work, energy, strength. They were not flotsam and jetsam carried by currents beyond their control; Bnai Yisrael charted its own course. (Ramban, Shemos 32:1).
However, Aharon miscalculated. They did not take responsibility for their current circumstances to better themselves. Instead, unprepared for their own significance, they worshipped at the altar of self-importance. If indeed the world was governed according to midas ha-din, if indeed they had through their own agency brought about their own circumstances, they could credit themselves and their own deservedness for their redemption from Egypt. (Ramban, Shemos 32:4). It was not God who took them from Egypt; it was the principle of justice — they deserved the redemption they got, and God had nothing to do with it. They worshipped their own virility, virtue, and vigor, exaggerated their control over reality, and deified the midas ha-din. They transformed the symbol of self-reliance into a cult of self-congratulation.
As punishment, God decreased the degree of His protection: He removed His Presence from their midst and directed an angel to lead them to the promised land. (Ramban, Shemos 33:3). Bnai Yisrael would thus be doubly free: free from Egyptian oppression, and free from God’s protection. This state of affairs was not ideal — it was after all, a punishment. But it was a punishment with a purpose: Bnai Yisrael would finally become self-reliant and self-governing.