If I was teaching children about the Atonement and one of them asked the question above, the simplest answer I would give is that humans need symbolism in their lives that are powerful and compelling.
I then would explain the symbolism of the scapegoat and talk about how powerful it is for a God to be the Great Scapegoat - especially in a culture at that time that used the scapegoat in its actual ceremonies. I would read the passages in Isaiah that deal most directly with his suffering. I would say that I have no clue whatsoever about the mechanics of the Garden of Gethsemane (exactly how Jesus actually suffered for our sins and weaknesses and mistakes and pain and every other bad thing we experience) - but I really love the idea and symbol of a Great, Loving, Suffering-Along-With-Us-to-Truly-Understand-Us God.
If I was talking with an older child who could understand deeper things, I would go into more detail about my own view of the symbolic vs. the literal, but for a younger child, I would keep it to the simpler outline above. If explained using age-appropriate vocabulary and visual images of a scapegoat, I believe most children who are out of the nursery could understand - at least to some degree.
An Early MormonAd: 1969
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