Stating things in this way, leaves a very important part of Christian story out of the picture. Salvation story can not be contemplated only like the payment of a ransom, but as a story of love.
Consider this from St Mark
And one of the scribes came, and hearing their argument together, and seeing that he had given them a good answer, put the question to him, Which law is the first of all? 29 Jesus said in answer, The first is, Give ear, O Israel: The Lord our God is one Lord; 30 And you are to have love for the Lord your God with all your heart, and with all your soul, and with all your mind, and with all your strength. 31 The second is this, Have love for your neighbour as for yourself. There is no other law greater than these. 32 And the scribe said to him, Truly, Master, you have well said that he is one, and there is no other but he: 33 And to have love for him with all the heart, and with all the mind, and with all the strength, and to have the same love for his neighbour as for himself, is much more than all forms of offerings. 34 And when Jesus saw that he gave a wise answer, he said to him, You are not far from the kingdom of God.
It is recognized that love to God and your neighbour is superior to any offering (sacrifice).
and then, this one from St John:
This is the law I give you: Have love one for another, even as I have love for you. 13 Greater love has no man than this, that a man gives up his life for his friends.
So Jesus is saying that He is going to undertake an act of love.
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