Why was Aaron, the brother of Mōšéh, not punished by death together with idolators (others who have sinned with the Golden Calf) when Mōšéh came from the mountain?
Why was Aaron treated differently?
The Gemara in Sanhedrin 7a says that Aaron's intention was noble. He saw that the Yidden had stoned Chur to death and realised if he opposed them he would meet the same end. By killing Aaron the Jews would commit an unparalleled crime, of Killing a Kohein Venovi. Just take a look at the retribution God exacted for the killing of Zecharyah, a Coheon Venovi. Aaron realised it would be better for them to serve idols then commit such a grave sin.
In addition Rashi says that he was hoping to delay them until Moses came and hoped that the women would put up a fight not to give up their jewelry so quick.
In the ancient Near East, gods were worshiped at their altars. This is where each god was thought to live - its altar. A very common decoration under the god was a gold bull or calf.
Although we wanted to worship an idol and were creating the calf to that end, Aaron had a different idea in mind. He wanted to create a throne for G-d. He said, "אֵלֶּה אֱלֹקיךָ יִשְׂרָאֵל" "This is your G-d, Israel," and gestured not to the calf, but to the space above the calf. Aaron knew G-d's true nature and was trying to use symbolism the Israelites would understand. But unfortunately, they failed to understand it and treated the calf as an god itself.
After some Googling, it seems this idea is advanced by Michael Coogan in A Brief Introduction to the Old Testament: The Hebrew Bible in its Context. From Wikipedia: