Sin separates us from God.
Because GOD is holy, He will not allow Himself to become corrupted by embracing sin or anyone who has committed sin.
Sin is that which GOD detests and His character will not allow Himself to abide with that which is stained by sin.
When a person sins, their soul becomes corrupted in GOD's eyes. The sin creates an internal conflict between the principles of GOD's nature. If He embraced the sin-stained soul (in their sins), He would no longer be holy. If He embraced some stained by sin but not others, He would no longer be just. He would have shown partiality, which His soul hates.
GOD spoke to Israel through the prophet Isaiah, saying:
2 But your sins stand between you and your God, and He turned His face from you because of your sins ...
(Isaiah 59:2a OSB)
This principle is clearly illustrated in the Garden of Eden. Initially, Adam and Eve enjoyed perfect peace with GOD there. Because of this, GOD gave them access to the tree of life, from which they could eat freely.
After they sinned, GOD banished them from the Garden and they no longer had access to the tree of life. This physical separation was a consequence of the severance of their harmonious spiritual relationship with GOD.
After being banished from the Garden, we immediately thereafter see that animal sacrifices had been introduced, for in Genesis 4, Abel offered from his flock to GOD.
In the first century A.D., the apostle Paul bluntly stated the fateful human condition this way:
22 ... There is no difference between Jew and Gentile, 23 for all have sinned and fall short of the glory of God,
(Romans 3:22b-23 NIV)
When Adam and Eve sinned, the curse of the knowledge of good and evil made temptation a reality for all humans of every generation. And our flesh is too weak to consistently resist these urges and evil desires. Every man and woman becomes a sinner, separated from GOD.