“What a waste!” We hate it when potential has been ruined. The Torah has a word for it: neveilah.
The word is first used by G-d in his plans to deal with the builders of the Tower of Babel:
Let us, then, go down and neveilah their speech there, so that they shall not understand one another’s speech.”
The people are irrevocably blocked from building their tower, and all their work is for naught. Their words, their speech, was turned by G-d into a wasted and misplaced effort, neveilah.
So, too, is the next use of the word in the text:
Meanwhile Jacob’s sons, having heard the news, came in from the field. The men were distressed and very angry, because he had committed a neveilah in Israel by lying with Jacob’s daughter—a thing not to be done.
Dinah was undone, ruined, as a result of this attack (her virginity was wasted, similar to Deut 22:21). There is a palpable sense of loss and regret when an entire promising life come down to one single (and awful) event. A neveilah is an event that annihilates potential, the opportunity for spiritual elevation. And so the word is commonly used to refer to an animal that has died in a manner (e.g. disease, predator, etc.) that renders it unusable for human consumption (according to the laws of the Torah). Kosher meat elevates the mind and body – and unkosher meat cannot achieve that spiritual result.
Fat from animals that are neveilah or were torn by beasts may be put to any use, but you must not eat it.
Or when a person touches any [spiritually blocked] thing (be it the neveilah of an impure beast or the neveilah of impure cattle or the neveilah of an impure creeping thing) and the fact has escaped notice, and then, being blocked from spiritual elevation, that person realizes guilt;
Such an animal cannot be elevated through their death, and they cannot elevate the mind and body of a person. From a practical Torah perspective, such an animal is just wasted. (An animal that killed in an offering or in a kosher manner for food is not neveilah. That animal has, through its death, achieved a higher purpose.)
Which helps explain the use of the word in the verse that we are pulling apart, word by word:
If any party is guilty of a capital offense and is put to death, and you string the body on a tree, you must not let the neveilah remain on the tree, but must bury it the same day
A person who has been killed that way is no good to mankind any more. And so it is called a neveilah, because of the meaning of its death. And the dead man might even be called a neveilah because of his life, a life which could surely have been lived otherwise, with different and better choices and ending. A terrible waste.
[Note that this is part of a series explicating a single verse: Deuteronomy 21:23. All work was done in collaboration with @susanquinn, @kidcoder, @blessedblackmith and @eliyahumasinter. The full series can be found on creativejudaism.org]