(It is worth noting that among the unkosher species there are also gradations. In particular the donkey has a higher level than other animals, as expressed in the requirement to redeem it, as we explained in a previous column (See SA YD 321). Another animal sometimes mentioned in Chasidic writings as having a somewhat higher nature than other forbidden species is the camel, which together with donkeys and kosher species formed part of Yaakov's gift to Esav in Bereshit 32. Both camels and donkeys extensively served the Patriarchs.)
Another prominent representative of the Breslav tradition, Rav Nachman Goldstein of Tcherin known as the Tcheriner Rav, gives a parallel explanation of the prohibition of abdominal fat, which applies to domesticated animals but not to wild ones or birds. (SA YD 64:1.)
We have often explained that the blood of animals embodies their lower, purely bestial nature. The Tcheriner Rav helps us refine this insight a little more: the blood represents one aspect of bestiality, namely cruelty, whereas the abdominal fat represents another aspect: stupidity and torpor.
Scripture often uses fat to signify these qualities, as in the verse: "And Yeshurun fattened and rebelled; you have become fat and thick and covered over; he has abandoned G-d his creator, and disgraced the Rock of his salvation" (Devarim 32:15).
This quality is particularly salient in the domesticated beasts, which as we pointed out are comparatively dumb and lacking in vitality and resourcefulness. We may also add that these animals are often intentionally fattened for slaughter. But the wild animals, called in Hebrew "chaya" meaning "lively", don't embody this kind of stupor and idleness. Thus their abdominal fat is permissible.
Rav Goldstein adds an additional reason wild animals and birds are less representative of our lower nature than domesticated ones: we can obtain them only with difficulty, by trapping them. Thus they embody vitality not only in their own resourceful existence but also in the fact that human effort and ingenuity are required in order to obtain them.
(Based on Nachat HaShulchan Yoreh Deah 28)