Scripture plainly teaches that Christ bears our sins (Isaiah 53:4, 11-12; I Peter 2:24; Hebrews 9:28). Yet, we introduce grave error if we gloss over either the Bible's general teaching on sin or whose sins, in particular, are atoned for in Leviticus 16.
One error lies in blaming Satan for the sins of humanity, then interpreting the azazel to represent Satan bearing mankind's sins. Apocryphal tradition holds that all sin should be ascribed to a fallen angel named Azazel, and even today it is commonly taught that the real cause—the actual author—of human sin is Satan. However, the Word of God shows that this is not true.
There is no question that Satan deceives (Revelation 12:9). He broadcasts his attitudes, and we all have tuned in to them. Ephesians 2:2 establishes that an evil spirit influence is at work in the world today. John declares that “the whole world lies under [his] sway” (I John 5:19).
However, “there is a spirit in man” that is the basis of mankind's reason and free moral agency (Job 32:8; I Corinthians 2:11). This biblically revealed truth means that, while a malignant spirit can affect the spirit in man, it does not force a person to act. This outside spirit gives people terrible information on which to base their decisions, but God says they have enough evidence of His power and divine nature to make them without excuse (Romans 1:20).
The ancient Israelites did not have God's Spirit, yet He still set life and death before them, commanding them to choose (see Deuteronomy 30:15-20). They had only the spirit in man, but the power to choose was still theirs. Earlier, God had warned Israel, “Take heed to yourselves, lest your heart be deceived, and you turn aside and serve other gods and worship them” (Deuteronomy 11:16; emphasis ours). God's admonition shows that if they allowed themselves to be deceived, it was due to their not “tak[ing] heed.” They could blame only themselves. Satan exerts influence, sometimes powerfully, but the responsibility to choose life still belongs to the individual.
When we sin, it is not because Satan authors it. James 1:14 says that we sin when we are drawn away by our desires, which give birth to sin (verse 15). We sin because our hearts are not yet like God's heart, which cannot be tempted. The core problem is not what Satan does—though it is certainly problematic—but the desperately evil human heart (Jeremiah 17:9). The solution is a new, spiritual heart like Christ's (Ezekiel 36:26).
The common view of Leviticus 16 holds that the goat being led away and released is a type of what happens to Satan. However, neither Satan's binding (at the beginning of the Millennium; Revelation 20:1-3) nor his being cast into the Lake of Fire (sometime after the Millennium; Revelation 20:10) corresponds with the azazel being set free. While not every symbol will necessarily match up in a spiritual fulfillment, it is hard to see how these things even begin to match up. The goat is commanded to be released (Leviticus 16:22), while the fallen archangel is confined, restrained, and (later) cast into fire—completely dissimilar actions. In short, there is no scriptural support for Satan fulfilling the part the live goat plays.