Contradiction with Exodus 32:4
It narrates that Aaron himself used a graving tool to make the molten calf, showing his direct involvement, while Exodus 32:24 implies that the calf simply emerged from the fire.
Exodus 32:4: And he received [them] at their hand, and fashioned it with a graving tool, after he had made it a molten calf: and they said, These [be] thy gods, O Israel, which brought thee up out of the land of Egypt.
Contradiction with Exodus 20:4
This verse directly commands not to make any graven images or idols, contradicting Aaron's action in Exodus 32:24 where he facilitated the creation of the calf idol.
Exodus 20:4: Thou shalt not make unto thee any graven image, or any likeness [of any thing] that [is] in heaven above, or that [is] in the earth beneath, or that [is] in the water under the earth:
Contradiction with Deuteronomy 9:16
This verse recalls how Israel made a molten calf and quickly turned away from God's commands, which contradicts Aaron’s account in Exodus 32:24 as it highlights intentional disobedience.
Deuteronomy 9:16: And I looked, and, behold, ye had sinned against the LORD your God, [and] had made you a molten calf: ye had turned aside quickly out of the way which the LORD had commanded you.
Paradox #1
Exodus 32:24 presents an explanation by Aaron that the golden calf came out of the fire on its own. This can be seen as inconsistent with the earlier description where Aaron actively casts the calf from melted gold. The contradiction lies in Aaron portraying a miraculous occurrence rather than acknowledging his role in crafting the idol.
Paradox #2
The contradiction in Exodus 32:24 could be that Aaron tries to avoid responsibility for making the golden calf by suggesting the idol simply appeared by chance. This shifts blame away from his active role, which conflicts with taking personal responsibility for one's actions.