Zevachim 10:3-4

Zevachim 10:3

A firstborn animal comes before an animal tithe because it is holy from birth and is eaten only by kohanim. An animal tithe comes before bird offerings because it is slaughtered and parts of it – the blood and the fats – are of greater sanctity (kodshei kodashim).

Zevachim 10:4

Bird offerings come before flour offerings because they are a type of blood sacrifice. The flour offering of a sinner comes before a voluntary flour offering because it is brought for his atonement. A bird sin offering comes before a bird burnt offering; the same is true when consecrating them (i.e., one designates the bird for a sin offering before the bird for a burnt offering).