John Lightfoot on Luke 2:24

[A pair of turtledoves, &c.] I. "The turtles were older, and of a larger size": pigeons less, and younger. For it is said of pigeons, two young pigeons; but not so of turtles.

This was called the offering of the poor; which if a rich man offered, he did not do his duty. And when the doctors speak so often of an offering rising or falling, it hath respect to this. "For the offering of the richer sort was a lamb; but if his hand could not reach to a lamb, then he offered a pair of turtles, or pigeons. But if he was poor, he offered the tenth part of an ephah: therefore is the oblation said to be rising or falling."

"King Agrippa came one day to offer a thousand burnt offerings; but a certain poor man prevented him with two turtledoves. So, also, when one would have offered a bullock, there was a poor man prevented him with a handful of herbs."

II. Of the two turtledoves or young pigeons, one was to be offered as a burnt offering, the other as a sin offering. But as to the particular appointment of the one for the burnt offering, the other for the sin offering, that is, which should be which, it is disputed among the doctors whether it lay in the breast of him or her that offered it, or the priest, to determine it.

By the way, we may observe that the blessed Virgin offers a sin offering for herself. Now what the meaning and design of a sin offering was, is evident from Leviticus 4 and 5.