Is Jesus Christ a sacrifice offered to us by the Father, or is he the solution to God's own problem?
We need to examine teaching in light of the Triune nature of God, for God is in an eternal communion of love; this is what the apostles teach us.
John teaches that the Father sent his only Son so that we may live through him.
Paul teaches us that the Father demonstrated his love for us by sending his only Son.
Also in Romans 3:25, Paul explains that it is the Father who gave the Son to us so that we might be justified in him and through him.
There is no explicit text in the teachings of the apostles and early Church Fathers stating that the Son paid the price for our sins to the Father, to God, or to Satan.
The sacrifice of the Son was offered by the Father not out of anger towards us, but for His own good. We were found naked, we were found sick, we were found poor, we were found dead—this is our corruption. Therefore He sent His Son to destroy death by death, so that we might live through Him and in Him.