Why wasn't Aharon punished by death together with idolators (others who have sinned with the Golden Calf) when Moses 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:
Another understanding of the golden calf narrative is that the calf was meant to be the pedestal of [G-d]. In Near Eastern art, gods were often depicted standing on an animal, rather than seated on a throne. This reading suggests that the golden calf was merely an alternative to the ark of the covenant or the cherubim upon which [G-d] was enthroned.
As I wrote here:
This question was raised by the medieval commentator Gersonides. He argues that Aaron was actually trying to prevent the idolatry, and did everything in his power to delay it as much as possible, hoping that Moses would return in the interim and sort things out. Here is the ESV translation of the relevant passage in Chapter 32:
1 When the people saw that Moses delayed to come down from the mountain, the people gathered themselves together to Aaron and said to him, "Up, make us gods who shall go before us. As for this Moses, the man who brought us up out of the land of Egypt, we do not know what has become of him." 2 So Aaron said to them, "Take off the rings of gold that are in the ears of your wives, your sons, and your daughters, and bring them to me." 3 So all the people took off the rings of gold that were in their ears and brought them to Aaron. 4 And he received the gold from their hand and fashioned it with a graving tool and made a golden calf. And they said, "These are your gods, O Israel, who brought you up out of the land of Egypt!" 5 When Aaron saw this, he built an altar before it. And Aaron made proclamation and said, "Tomorrow shall be a feast to the LORD." 6 And they rose up early the next day and offered burnt offerings and brought peace offerings. And the people sat down to eat and drink and rose up to play.
Thus, Gersonides argues that first Aaron told them to get the jewelry from their wives and children, knowing that this would take a while as the women and children would be very hesitant to give up their jewelry. When Moses still hadn't returned, Aaron dragged out the process further by "fashion[ing] it with a graving tool". When Aaron then saw that Moses had still not returned and the people had begun referring to the calf as "gods", he delayed further by building an altar. When this was still not enough he delayed again by saying "Tomorrow shall be a feast to the LORD." But the next morning the people arose and brought offerings and there was nothing more that Aaron could do.
Gersonides argues further that Aaron could not have objected outright to the idea because then the people would have simply killed him and there would be nothing left to temper their idolatry. If Aaron remains alive he at least has the ability to be undercover and try to minimize the great sin that was to take place.
The Abarbanel (Bamidbar 20:1) offers a novel approach to why Moshe and Aharon were serverly punished by the mei merivah. He cites many different approaches ,but rejects them and offers his own idea. He holds that they were punished for their 2 severe sins. Moshe for sending spies and Aharon for his part in the egel. However,the Abrbanel explains they weren't punished at the time of the others only for the sake of their honor. Therefore ,the reason why the punishment at mei merivah was so severe was because they were getting punished for other sins. So according to the Abarbanel Aharon was held accountable for the egel.
The Binyan Tzion(Rav Nasan Mass) on Sanhedrin 7a says that Aharon was not praised for his particpaition. In fact the gemara itself says that one should not praise such a compromise,since such a compromise is an insult to God.