A lecture I had recently highlighted the relational aspect of sin. And some things I've read recently spurred me to think about this so I've been thinking about it a good bit.
It is true that sin (wrongdoing, wickedness, evil) has a legal aspect. For example: breaking a law. When you break a law, you become guilty of a crime. Every person has disobeyed God's commands and each person deserves punishment. God loves justice and hates evil and wrongdoing. There is a need for each person to be made righteous (innocent, blameless, good). This idea of "justification" is a key doctrine of the Christian faith. It seems though that Westerners frequently emphasize this aspect of sin over and above others. But there is another side to sin.
There is a rift between God and man, and it is relational. We may have seen some Good News presentations like the bridge diagram, a great illustration of separation from God. But this separation is not just legal; it involves relational estrangement from the heavenly Father.
Christ came to do a whole host of things, one of the primary of which is to bring humanity into a right relationship with God. Through their disobedience, Adam and Eve broke the intimate parent/ child relationship they had with God. The problem since then has been how humans can restore the broken relationship. Through faith, and specifically in Christ, God the Father takes initiative and reconciles us to Himself (re-establishes relationship, gives us a peaceful relationship with Him).
When I do something against a loved one, my wife or daughter for example, they want restoration. We all want restoration. Its terrible to live in close proximity with someone you love and have tension arising from brokenness in the relationship. In human terms, divorce, parents cutting off their children (and vice versa) or friends no longer being friends are all manifestations of irreconcilable relationships.
God uses the sacrifice of Christ to restore the broken relationship, and the relationship is key. John 3:16 doesn't say, "For God so needed to restore justice to the universe that He gave His only Son." But this verse, maybe the most well known verse in the Bible says, "For God loved the world with such a great love that He gave His one and only Son so that anybody who trusts in Him won't die the everlasting death but will instead have everlasting life" (my paraphrase).
God loves people and thus reaches out to us in love. While it is true that "whoever believes is not judged" (John 3:18) it also true what John says in his first letter: "See how great a love the Father has bestowed on us, that we would be called children of God" (1 John 3:1). Jesus speaks clearly about hell and judgment, but He does so because God doesn't want people to experience these things.