Jacob Neusner, The Midrash: An Introduction (Northvale: Jason Aronson, 1990) 59.
Neusner quotes Sifra Leviticus, Parashah 7:14:1 (fourth century C.E., according to the Encyclopedia Judaica), which interacts with Leviticus 1:14-17:
"The priest shall bring it to the altar, pinch off its head": Why does Scripture say, "The priest...pinch off...?" This teaches that the act of pinching off the head should be done only be a priest.
This stood out to me because Leviticus 1:2-6 requires the worshiper to slaughter and flay the male from the herd before it's offered as a burnt offering. I'll use the King James Version here because it's more literal than what I usually use, the NRSV:
Speak unto the children of Israel, and say unto them, If any man of you bring an offering unto the LORD, ye shall bring your offering of the cattle, even of the herd, and of the flock. If his offering be a burnt sacrifice of the herd, let him offer a male without blemish: he shall offer it of his own voluntary will at the door of the tabernacle of the congregation before the LORD. And he shall put his hand upon the head of the burnt offering; and it shall be accepted for him to make atonement for him. And he shall kill the bullock before the LORD: and the priests, Aaron's sons, shall bring the blood, and sprinkle the blood round about upon the altar that is by the door of the tabernacle of the congregation. And he shall flay the burnt offering, and cut it into his pieces.
When a man offers a male from the herd as a burnt offering, he himself must slaughter and flay it. When a man brings a bird, however, the priest is the one who pinches off its head and tears it open.
Why the difference? I can't find the answer in my commentaries here, but I'll speculate (and perhaps wax homiletical in the process).
In Leviticus 5:7, we read that a person who can't bring a lamb for a trespass offering must bring two birds. So the richer Israelites offer animals from the herd, whereas the poorer ones offer birds or grain (if they're especially poor).
Maybe God wanted the richer Israelites to play a more active role in their sacrifice to teach them to place God above their riches. If they simply came and gave the animal to the priests so they could kill it, they wouldn't feel the sacrifice as deeply. They'd just come, give their animal, leave, and pat themselves on the back for appeasing God. But God wanted them to play a more active role in the worship, to get their hands dirty, for he realized that the rich are in danger of forgetting God (Deuteronomy 8:11ff.).
I wonder how biblical scholars or ancient Jewish interpreters address this issue.