A strung-up body is a curse of God.
What does this mean? How is a body that is strung up a curse of G-d? Indeed, the verse is so odd that translations cannot even agree if the curse is of the hanged man, or a curse of G-d, or by G-d, or under G-d… What is clear is that a curse is involved. But why?
We can start by understanding that the first time the word for “curse” is found in the Torah is with Rivkah and Jacob:
If my father touches me, I shall appear to him as a trickster and bring upon myself a curse, not a blessing.” But his mother said to him, “Your curse, my son, be upon me! Just do as I say and go fetch them for me.”
What did they do to bring the curse down? It might be for the willful deception. But I think in this case, it might also be for interfering in the relationship between a father and son, for getting in the middle of an opportunity for a relationship to grow. Esau serving his father was to be an act of honoring his father, a holy act of growth. Interrupting that act thus earned a curse.
This might explain why leaving a body strung up on a tree creates a curse. Each person is, after all, given a soul which is comprised of the divine breath: G-d formed the Human from the soil, blowing into his nostrils the breath of life: the Human became a living being.
But a body that is hung has its breath trapped within it (a noose stops breathing).
Perhaps the Torah is telling us that an unburied body, with its breath trapped within it, has a soul that cannot return to G-d?! And in that case, anyone who blocks the return of a human soul is acting just as Rivkah and Jacob did, by interfering with someone else’s relationship.
Each person has a soul on loan from G-d. When we die, the soul is meant to return to its source (what happens after that is not told to us in the Torah). And so we should be sensitive to the fact that G-d seems to want human souls returned, even for murderers who were justly executed.
The Torah seems to be making an even bolder and more general statement: that we, as people, are capable of creating a curse merely by interfering with the lives of others, with the relationships between other people, or the relationships between man and G-d.
If this is correct, then the meaning of this verse spawns thousands of ripples. It helps explain why Judaism is so careful about loshon horah, gossip or slander or negative speech of all kinds. It tells us that getting between a father and son, or a husband and wife, or two brothers, is analogous to getting between someone and their connection to G-d. A religion that seeks to foster holy relationships of all kinds is naturally keenly interested in not obstructing those very same relationships!