Chullin, Chapter 1, Mishnah 6. Our mishnah continues the pattern of the two mishnayot before it: it lines up five pairs of subjects that resemble one another closely, yet when we look at one particular halachic detail, what qualifies in the one case is precisely what disqualifies in the other. There is no overlap at all.
Parah Adumah and Eglah Arufah
The opening pair reads: "Kasher beparah", whatever renders the red cow fit, "pasul ba'eglah", disqualifies the calf; "kasher ba'eglah", whatever renders the calf fit, "pasul baparah", disqualifies the cow.
The parah adumah is a red cow with which no labor was ever performed. Once burned, its ashes serve to purify a person, or an object, that has contracted tumah from a corpse. The eglah arufah belongs to a completely different situation. A murder victim is discovered in open country between towns and the identity of the killer is unknown. The great Sanhedrin measures the distances to establish which town lies closest, and the elders of that town, the ziknei ha'ir, take a calf and kill it by severing its nape from behind, an act known as arifah. They then wash their hands and declare publicly that this blood was not shed by them.
Both of these are forms of korbanot, and both share a striking feature: neither takes place inside the Beit Hamikdash. Both animals are killed outside it, which is why the mishnah finds them comparable. And here is exactly where they diverge. The parah adumah requires ordinary shechitah, slaughter at the front of the neck. The eglah arufah requires arifah, breaking the neck from behind. Shechitah, the very thing that makes the parah adumah valid, would render the eglah arufah unfit. Arifah, the very thing the eglah arufah demands, would render the parah adumah unfit.
Kohanim and Levi'im
The second pair: "Kasher bakohanim", that which qualifies a kohen, "pasul balevi'im", disqualifies a Levi; "kasher balevi'im", that which qualifies a Levi, "pasul bakohanim", disqualifies a kohen. Here the mishnah shifts to the men who staffed the service in the Mishkan and in the Beit Hamikdash.
Once a Levi turned fifty he was no longer eligible for service in the Mishkan. The Mishkan was the portable Sanctuary that served the nation before the permanent Beit Hamikdash was built, and across the years of travel through the midbar it was taken down and put back up over and over again. That heavy labor fell to the tribe of Levi, and by fifty a man's strength was generally no longer equal to it. A second disqualification applied as well: a Levi whose voice had thinned with the years, since the singing in the Beit Hamikdash was theirs to perform.
Kohanim were never disqualified for either of these reasons. Neither advancing years nor a weakened voice removed a kohen from the service. Kohanim, however, were disqualified by something else entirely: a physical blemish. And a blemish has no bearing whatsoever on a Levi.
So the contrast is complete. Age and a weakened voice, which leave a kohen perfectly fit, disqualify a Levi. A blemish, which leaves a Levi perfectly fit, disqualifies a kohen.
One clarification is worth adding. The Levi's disqualification at fifty applied only to service in the Mishkan. In the Beit Hamikdash he could continue to serve, since the permanent Sanctuary was never dismantled and carried, and the heavy labor that defeated an older man simply did not exist there.
Earthenware Vessels and All Other Vessels
The third pair turns to vessels: "Tahor bikli cheres", what leaves an earthenware vessel pure, "tamei bechol hakelim", renders every other kind of vessel impure; and "tahor bechol hakelim", what leaves all other vessels pure, "tamei bikli cheres", renders earthenware impure.
When a source of tumah makes contact with the outer wall of an earthenware vessel, the vessel remains tahor. Vessels of any other material behave otherwise: touch them anywhere at all, the outside included, and they contract tumah. In the reverse direction, let a source of tumah pass into the hollow airspace of an earthenware vessel and that vessel is rendered tamei though nothing ever touched it, while a vessel of another material stays pure in such a case until genuine contact takes place.
The result: contact with the outside leaves earthenware untouched but renders an ordinary vessel tamei, while entry into the air space renders earthenware tamei but leaves an ordinary vessel entirely unaffected.
Wooden Vessels and Metal Vessels
The fourth pair: "Tahor bikli eitz", what leaves a wooden vessel pure, "tamei bikli matachot", renders a metal vessel impure; and "tahor bikli matachot", what leaves a metal vessel pure, "tamei bikli eitz", renders a wooden vessel impure.
A wooden vessel is capable of contracting tumah only if it has a beit kibul, a receptacle able to hold something, as a spoon does: even a spoon holds a small amount of liquid. A metal vessel, by contrast, can become tamei even when it is entirely flat, such as a knife. On the other side of the equation, a metal vessel that is unfinished, usable but not yet fully completed, cannot become tamei, whereas an unfinished wooden vessel can.
So having a receptacle is what makes a wooden vessel susceptible to tumah, and it makes no difference at all to metal. Being fully completed is what makes a metal vessel susceptible, and it makes no difference at all to wood.
Bitter Almonds and Sweet Almonds
The fifth and final case of our mishnah concerns two varieties of almond, the bitter and the sweet. Recall the underlying principle: terumot uma'asrot are separated only from produce that is edible. That principle is what drives the whole comparison.
The mishnah states: "Hachayav bishkedim hamarim", that which is obligated in terumot uma'asrot when the almonds are bitter, "patur bametukim", is free of the obligation when they are sweet; "hachayav bametukim", that which is obligated in the sweet variety, "patur bamarim", is free of the obligation in the bitter.
Bitter almonds count as food only while they are still small, and at that stage they carry the obligation of terumot uma'asrot. Sweet almonds become fit to eat only after they have grown large. So while the almonds are small, the bitter ones qualify as food and are obligated, and the sweet ones, not yet fit to eat, are exempt. Once the almonds reach full size the picture reverses: the sweet ones are now food and obligated, and precisely at that stage the bitter ones carry no obligation.