Kommentar zu Kinnim 2:2

פרח – one pigeon from this [pair of unassigned birds] to the other woman’s [pair of unassigned birds].

Introduction This mishnah explains the end of yesterday's mishnah.

פוסל אחד בהליכתו – from the place that it separated itself. And it invalidates it itself or another from the place where it became mixed. For when one pigeon flew out from two couples of birds to two other couples of birds, there are three pigeons alone and five pigeons alone, but from three pigeons, one is not able to sacrifice only two, one for a burnt-offering and one for a sin-offering, for if he would make two of them burnt-offerings it is fund that the third that remains was fixed/established, and that one (i.e., pigeon) which flew away is for a sin-offering, and he is not able to offer any further from the five individual pigeons, other than the two sin-offerings, according to the law of sin-offerings that were mixed with an obligatory offering, as we stated in the first chapter (see Tractate Kinnim, Chapter 1, Mishnah 2), that is not kosher/fit other than the number of sin-offerings that is part of the obligatory offering. Alternatively, one does not offer up [as a sacrifice] the third that remains, for we are concerned that perhaps that they will offer up the one that flew away with the five single pigeons and make it is a sin-offering, and his fellow that remains with three individual birds will also make it a sin-offering, and it is found that there will be two sin-offerings from one couple of sacrificial birds. And similarly, from the five individual pigeons he is not able to offer only two sin-offerings and two burnt-offerings, for if he made three sin-offerings or three burnt-offerings, perhaps he would make them from two couples of sacrificial birds of one woman, and there is no law of two couples of sacrificial birds other than with two sin-offerings and two burnt-offerings, and that is that is it invalid – it or another [bird] in the place where it was mixed, and it invalidates the other [bird] that is corresponding to it from the place that it flew off and was separated from there.

How is this so?
Two women, this one has two pairs and this one has two pairs, and one bird flies from the [pair of] one to the other [woman's pair], then it disqualifies by its escape one [of the birds from which it flew]. Two women each have two pairs of birds. If one bird flies away from one woman's two pairs, and joins the second woman's two pairs, the woman who is left with three birds can only use two. Of the three birds remaining, she can offer one as a hatat and one as an olah, but the third cannot be offered as either an olah or a hatat, for if she were to offer the one that remains as a hatat, then the one that flew away would have to be an olah. And when it joins two kinim, only two of the five could be offered as olot (the minimum number of olot in the two pairs see 1:2). The same would be true if she were to offer the third as an olah the one that flew away would be a hatat, and the second woman can only offer two birds as hataot. But when the woman with three birds offers only two of them, the other woman can still offer two hataot and two olot. The woman with five birds also cannot take another bird and make three pair, offering one as an olah and one as a hatat from each pair, lest the fifth bird actually be one of her original birds and if she offers it as a hatat, it is possible that she will offer three hataot from her original four birds (one with the new pair, and two as the original pairs). For the same reason, she can't take another bird and offer the fifth bird as an olah, lest it turns out there are three olot from the original four birds. She has no choice but to offer only four birds. In the end, it turns out that of the original eight, the woman whose bird flew the coop offers one pair, and the woman to whom the bird flew offers two pairs. Two birds go to waste.

If it returned, it disqualifies yet another by its return. If one of the five birds flies back to the other three birds, it disqualifies one of the birds that it left. Of the four left with woman two, she can offer only two of them, one as an olah and one as a hatat. She can't offer more lest the bird that went back to woman one is not the same bird that joined her group, and she only has three birds left from her original two kinim.

חזר פוסל אחד בחזרתו – it (i.e., the original bird who flew off) returned and one of the five individual pigeons flew off into [this group of three], that it was now found four individual pigeons from here and four individual pigeons from there. The one through its return invalidates from the place that it separated from and left from there, and it or another are invalid in the place where it mixed there, and the cannot offer up other than one sin-offering and one burnt offering from the four that are here, and one sin-offering and one burnt-offering from the other four. For perhaps, that individual pigeon that flew away second is from the same two couples of sacrificial birds and is not the one that became mixed in it initially, and there remained there three individual pigeons from the two couples of sacrificial birds and that one that flew away there first, and similarly in the second place. But if he made in one place two burnt-offerings and one sin-offering, that [bird] which flew away to the other side would be set for a a sin-offering offering and he would not be able to offer up there [anything] other than one sin-offering, for perhaps, all thee sin-offerings that were made from here and there will be from two couples of sacrificial birds of one woman, therefore, one makes in every place one burnt-offering and one sin-offering, or two burnt-offerings and one sin-offering on this side and one sin-offering on that side, or two sin-offerings and a burnt offering on this side, and on the second side one burnt-offering, but if they returned and mixed together, always, there won’t be for them less than two couples of sacrificial birds that are fit/kosher.

If it flew away again and then returned, and again flew away and returned, no further loss is incurred, since even if they had all become mixed together, not less than two [pairs would still be valid]. This process of disqualification does not continue if birds keep flying back and forth between the kinim. For even if all four kinim get mixed up, he can always offer four birds, two as hataot and two as olot, as we learned in 1:3 that if four pairs of birds get mixed up, each woman can offer two birds, one as a hatat and one as an olah.