I would say that it also has to do with relationship with God.
Back with Adam and Eve, God had a good relationship with Mankind, but Mankind fractured that good relationship with sin, And from then on, Man had a shaky relationship with God as a natural consequence of sin. The animal sacrifices weren’t good enough to amend the relationship. It’s like trying to amend a relationship by buying gifts, it doesn’t really do anything.
To be able to amend the relationship between God and Mankind a sacrifice had to be made on God’s part, because Mankind with its flaws, is not capable of amending such a relationship. So, God humbled himself, becoming incarnate by the power of the Holy Spirit and was brought into the world through the Blessed Virgin Mary. By becoming one of us, God is able to come down to our level and reintroduce himself to us in a way that we can relate to. By doing this, those who followed Jesus were able to trust in God’s power again, instead of reverting to powerless idols. God showed us his ultimate love and affection for us by sacrificing himself on the cross and dying for us.
This is like a friend reaching out and giving of himself/herself to amend a relationship instead of relying on cheap gifts. This is how a relationship is really mended, by each side giving of themselves, and loving each other. This is what God did for us.
And God continues to reach out to us, and the way we reach back is through Christ, his message and his sacrifice.
Because of the mended relationship, people who amend their personal relationship with God are able to attain an eternal life with him, the source of life, love, and happiness.
My 2 cents.