Paul's most obvious mistake of logic was that he failed to apply Jesus' own message of a loving God to Jesus' death, and compounded his mistake when he failed to remove his Jewish beliefs from his interpretation of Jesus' death. Paul failed to grasp how immediately and directly applicable Jesus' message of God's unconditional, unwavering, eternal love was to Jesus’ own death. It seems obvious and inescapable now that Jesus' revelation of God's true nature must he used to interpret Jesus’ own life and death!
Paul's second mistake of logic involved a broad assumption he made about "the will of God." It appears that Paul became caught up in the emotional drama of Jesus' death, which caused him to overlook another very serious error in his interpretation. Paul correctly concluded that God allowed the death of Jesus, but Paul incorrectly assumed that God actively willed Jesus’ death to occur, as though it were a part of Jesus' mortal life plan to end that way. What Paul didn't see was that God allowed Jesus' death to occur by not willing to intervene in the development of events that precipitated Jesus' death. Neither God nor Jesus intervened because doing so would have violated the will-decision of the men who decided to have Jesus killed.
Just as Paul assumed that Jesus' death was an expression of God's active will, we can as easily assume it was an expression of God's passive will. It is logical to conclude that the death of Jesus was willed by God, and reasonable to conclude that it was passively willed to occur, but not actively willed to occur.
Paul's third mistake of logic is a continuation of the erroneous traditional Hebrew belief that our actions toward God can change God's performance for or against us: Our sinfulness will change God's nature of loving and compassionate forgiveness to anger and wrath; and, our actions to appease God's anger and wrath can return God's loving, forgiving behavior toward us. In effect, these two situations set up a relationship of manipulation between people and God. These two situations make God look like a naïve, doddering old fool.
Paul's mistake was that he continued to see God's love for His human children as conditional. Paul compounded his error by setting God up as the creator of the sacrifice needed to save the world — by giving up His Son to death and suffering! That is both illogical and irrational.
The reality of The Eternal Creator is that God's love for us is unconditional. God forgives us because that is an aspect of love — compassion and mercy — and that does not change! Therefore, there is no need for sacrifice of any kind. The reality of our Eternal Creator is that he so loved the world that he provided His Son to live among us, giving us an example of how to live.