Vayikra: Sefer HaChinuch: Mitzvah 128 – Concept 354
“He shall bring them to the Kohen, who shall offer first the one that is for a sin offering. He shall nip its head at its nape, but not separate it. (Leviticus 5:8) The Kohen may not decapitate
a fowl brought as a sin offering. (Rambam, Hilchot Ma’aseh HaKorbanot – The Laws of Sacrificial Procedure)
The Sefer Hachinuch explains that since this is the offering of a poor person, it must be performed as quickly as possible so that the person can go out and earn a living.
This is another reminder of how sensitive the Kohen must be to the person bringing the offering.