Therefore, the rule is that whenever the Altar does not get the right to the meat, the kohanim do not get the right to the hide. However, if an offering was valid even for some time, so that the Altar got the right to the meat, the kohanim acquired the right to the hide. This rule is derived from a phrase "the burnt offering of a man." Since the rule would be also true for a woman, the extra word "man" teaches us that it was valid for men to eat.
Hides of regular offerings, such as a peace offering, belong to their owners. Hides of all most holy offerings other than the burnt offering also belong to the kohanim, and this is derived through logic: if in the case of a burnt offering, where the kohanim do not eat the meat, the hide nevertheless goes to them, then for a sin offering, where the kohanim do eat the meat, certainly the hide goes to them.
Art: Pieter Gysels - Still Life with Vegetables Meat Fruit and Game