Parah, Chapter 8, Mishnah 3. This chapter collects cases in which tumah travels in a surprising direction, and it returns again and again to one striking formulation: the thing that made you tamei did not make me tamei, yet you made me tamei. Our mishnah applies that refrain to a group of people who are occupied with holy service and nevertheless emerge tamei from it.
The ruling arrives in two halves. First: "Hasoref parah uparim", whoever burns the parah or the bulls, "vehameshale'ach es hasa'ir", and whoever escorts the goat out of the camp, "metamei vegadim", conveys tumah to the clothing he is wearing. Then comes the contrast: "Parah uparim", the parah and those bulls themselves, "vesa'ir hamishtale'ach", along with the goat that is led away, "atzman ein metam'in begadim", carry no such power at all, and garments that come into contact with them remain tahor.
Which cow, which bulls, and which goat is the mishnah speaking about? The cow is the parah adumah, whose burning renders the one who performs it tamei. The bulls are the korbanos that were taken outside and burned: the bull of Yom Kippur, the bull brought for an inadvertent sin of the community, and the goat brought in connection with idolatry. The goat that is dispatched is the sa'ir hamishtale'ach, the goat sent off on Yom Kippur, and the man who leads it away likewise becomes tamei.
Here is the oddity. These men become tamei through their involvement with the animal, and their tumah is strong enough that it passes into the garments they are wearing. Yet the animal itself, the parah, the bulls, the dispatched goat, has no power to render garments tamei at all. The chain of tumah becomes stronger, as it were, one step down the line rather than weaker.
This is precisely why the mishnah signs off with its trademark declaration: "Harei zeh omer", this one speaks up and says, "metamecha lo tim'uni", whatever it was that conveyed tumah to you would have left me perfectly tahor, "va'atah timeisani", and yet you have gone ahead and conveyed tumah to me. Imagine the clothing addressing the man who did the burning or the escorting: direct contact with the animal itself would have left the garments untouched, and it is solely their contact with him, the person whom that animal rendered tamei, that brought tumah upon them.
The same phrase appeared in the preceding mishnayos of the chapter, and it is the thread that ties these cases together: tumah does not always weaken as it spreads, and the halachah measures each case by its own rules rather than by our expectations.