How does the (life and) death of Jesus atone for our sins?

The Jews before Jesus believed that blood had redemptive powers:

all things are cleansed with blood, and without shedding of blood there is no forgiveness

(Hebrews 9:22)

To regard a substance as having such abstract powers invariably comes from a form of thinking known as sympathetic magic. JG Frazer’s The Golden Bough (1889) extensively documents and elucidates such rituals. The Jewish belief in the abstract restorative powers of blood stems from a naive essentialism that should be anathema to the modern educated mind:
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