How the atonement works (short version)

Sin isn't like a crime where you go to prison for a certain amount of time and then get let out. It is a willingness to commit an evil act, whether or not we actually do. Sin is having bad intentions to act towards others and God (1 John 3:15; Matt 5:27-28). That's why sin goes away when someone repents. If you change your behaviour for the better, then you no longer have bad intentions in that area. So no more sin in that area.

A person can theoretically have perfect intentions, which would get rid of sin. But no one can do this in practice.

Another option is for God to swap our evil intentions for someone else's perfect intentions.

All it would take to make someone perfect is to get them not to resist this process.

God had to be born as a human to perform this 'swap', because a) only God's soul, in a human, could choose to have perfect intentions, and b) God the Father cannot receive our evil intentions (bear sin) but God as a human can (Isa 59:2; Hab 1:13).

In the atonement, Jesus took on (but did not endorse or have himself) an infinite number of bad intentions, multiplied over every possible eternity that humans could have lived in, for billions upon billions of minds, to fully swap our evil intentions for His perfect intentions forever. God has chosen the atonement to take full effect at a future date (Eph 1:13-14).

Longer version.