Adam Clarke on Hebrews 13:11

For the bodies of those beasts - Though in making covenants, and in some victims offered according to the law, the flesh of the sacrifice was eaten by the offerers; yet the flesh of the sin-offering might no man eat: when the blood was sprinkled before the holy place to make an atonement for their souls, the skins, flesh, entrails, etc., were carried without the camp, and there entirely consumed by fire; and this entire consumption, according to the opinion of some, was intended to show that sin was not pardoned by such offerings. For, as eating the other sacrifices intimated they were made partakers of the benefits procured by those sacrifices, so, not being permitted to eat of the sin-offering proved that they had no benefit from it, and that they must look to the Christ, whose sacrifice is pointed out, that they might receive that real pardon of sin which the shedding of his blood could alone procure. While, therefore, they continued offering those sacrifices, and refused to acknowledge the Christ, they had no right to any of the blessings procured by him, and it is evident they could have no benefit from their own.