Kinnim, Chapter 2, Mishnah 1. The first chapter dealt largely with pairs of birds that became mixed with other pairs, and with the question of which korbanot can still be offered. This second chapter opens by tracking a single bird: what happens when one bird of an obligatory pair disappears, dies, or flies off into a different group of birds entirely.
A reminder: the ken setuma
One who owes a two-bird offering must have one of the birds serve as a chatat and the other as an olah. Still, at the moment he sets them aside he is under no obligation to declare which role belongs to which. That determination may be left to the kohen at the time of the avodah. The bird the kohen appoints for the chatat is thereby the chatat, and its companion is automatically the olah; and should he appoint one of them for the olah, the other has by that act become the chatat.
Until that designation is made, the two birds are called a "ken setuma," a sealed or undesignated pair. They already carry the sanctity of a korban, but they do not yet carry the specific identity of chatat or of olah. Our mishnah asks what becomes of such a pair when one of its two birds is no longer available to be offered.
The three cases of loss
The first case in the mishnah: an undesignated pair, and of its two birds, "sheparach mimena gozal la'avir," one fledgling took wing into the open air. It got away, and there is no retrieving it.
The second case: "o sheparach lebein hametot." The bird flew into a flock whose members are all condemned to perish. This sends us back to the second mishnah of the opening chapter, where we saw that if a chatat bird gets mingled among olah birds, the whole assortment is abandoned to death, since identification has become impossible and not one of them may go up on the altar. Our escaped fledgling has now joined precisely such a doomed flock. It can never be singled out again, so it shares their fate and will never come as a korban.
"O shemet echad mehen," or no bird flew off at all, but one of the two simply died.
In all three cases the result is the same in one respect: one of the two undesignated birds is gone for good and will not be brought on the altar. The question is what happens to its surviving partner.
The ruling: he takes a second partner
The mishnah answers: "yikach zug sheni," he acquires a partner for the second bird. The owner is not required to set aside a fresh pair of birds from scratch. The loss of the first bird does not carry the surviving bird down with it; the survivor retains its standing and remains fit to be offered. The owner simply brings one additional bird to join it, and together they once again form a complete undesignated pair for his obligation.
When the bird flies into birds that will be offered
Until now we dealt with a bird that was lost to us entirely. The mishnah now turns to a bird that is not lost at all, but has flown into a group of other undesignated birds that are themselves waiting to be brought as korbanot: "parach lebein hakeirovot." The bird is standing right in front of us, but we can no longer tell it apart from the birds it joined.
The halachah is: "pasul uposeil echad kenegdo." The intruding bird is disqualified within the group it entered, and it also disqualifies one corresponding bird in the group it left behind.
Why should this be? Consider the situation. Of the original pair, only one bird flew off, and one bird remains in the owner's hand. If he now offers the bird in his hand as a chatat, then by that very act the bird that flew away becomes an olah. If he offers the bird in his hand as an olah, then the bird that flew away becomes a chatat. But the bird that flew away is now indistinguishable from all the other birds in the second group, so we have no way of knowing which bird there has been given which identity, and therefore we cannot proceed to bring the korbanot of that group with any confidence. Everything there hangs on what he does with the bird still in his possession.
The resolution is to limit the damage. One bird in the group that was joined is treated as disqualified and set aside, and the surviving bird of the original pair, the one corresponding to the bird that flew, is likewise disqualified. Once those two are removed from the picture, the remaining birds in the second group can be offered.
The mishnah formulates this as a general rule: "shehagozal haporei'ach pasul uposeil kenegdo," the bird that flies away is itself disqualified and it disqualifies its counterpart. Whenever an undesignated bird moves from one group of undesignated birds to another, one bird in each group is lost to the altar and must remain unoffered, while all the rest are still brought.
A word on the masechet
It is worth saying plainly that Masechet Kinnim is among the most difficult masechtot in all of Shas. Behind each of these rulings lies an enormous amount of technical detail that we are not able to unfold here. If a piece of it does not settle in the mind at first pass, that is not a failure of the student; it is the nature of the material.