Chullin, Chapter 1, Mishnah 5. The mishnah before ours ended with two mirrored rulings: whatever qualifies for shechitah is disqualified for melikah, and whatever qualifies for melikah is disqualified for shechitah. Our mishnah, along with the next one, keeps that same balanced formulation going, even though the subject has left shechitah behind. The topic now is the two kinds of birds that may be offered on the altar: the turtledove (tor) and the young pigeon (ben yonah).
In the words of the mishnah: "Kasher b'torin pasul bivnei yonah" - whatever qualifies a turtledove disqualifies a young pigeon. And the mirror image: "Kasher bivnei yonah pasul b'torin" - whatever qualifies a young pigeon disqualifies a turtledove.
What is the distinction? It is a matter of age. Turtledoves are fit for the altar only once they have reached full maturity. Young pigeons are the opposite: they are fit only while they are still young, before maturity sets in. So the very quality that qualifies the one disqualifies the other. Once full maturity arrives, which is precisely what the turtledove requires, that same maturity renders the pigeon unfit. And during the stage of youth, which is precisely what the pigeon requires, the turtledove cannot yet be offered. The two windows of validity do not overlap at any point.
The mishnah then adds a third clause: "Techilat hatzihuv bazeh uvazeh pasul" - the onset of yellowing is invalid in both cases. This refers to the transitional stage between youth and maturity in these birds, identified by the feathers around the neck beginning to turn yellow. At that midpoint, neither species may be brought.
The reason is straightforward once the two requirements are held side by side. The turtledove at this stage is still too young, since it may be offered only when fully mature. And the pigeon at this stage is already too old, having passed out of youth, and so it too can no longer be offered. The same moment in a bird's development that leaves one species not yet eligible leaves the other no longer eligible.