Why did the Israelites want Aaron to make them a god?
While Moses was up Mount Sinai for about thirty days, the Israelites grew uncertain because he had disappeared from their view. Having left Egypt, they claimed they had no gods, so they asked Aaron to make them one. Their request arose from Moses' prolonged absence and their sense of having no visible deity.
Les explains that while Moses was up in the mountain, the children of Israel asked Aaron, "Make us a god." They said that since leaving Egypt they had no gods, and they did not know what had happened to Moses, who had disappeared up the mountain. Moses had been gone a few weeks and would be gone for a total of thirty days. Aaron said he threw gold into the fire, and out came the calf; then they began worshiping the golden calf. Their dancing was lewd, lascivious, and naked pagan worship.