Parah, Chapter 7, Mishnah 2. This chapter deals with the melachos, the acts of labor, which render the water of the chatas unfit from the time it is drawn until the ashes of the parah are placed into it. Our Mishnah teaches that drawing the water is itself an act which can clash with another act of labor, and that this holds true even when the water is being drawn on someone else's behalf.
The Mishnah presents its cases one after another. "Hamemaleh be'achas yado", someone who fills the vessel using only one of his hands, "ve'oseh melachah be'achas yado", while his other hand is occupied with an act of labor. Next: "Hamemaleh lo ule'acher", he fills at a single moment both for himself and for a second person, "o shemilei lishnayim ke'achas", or the two portions he fills together belong to two other people. Concerning all of these the Mishnah rules "sheneihem pesulim", neither portion of water may be used. And the principle behind the ruling is stated: "shehamelachah poseles bamiluy", an act of labor ruins the drawing of the water, and this applies "bein lo bein le'acher", whether the water he is drawing belongs to him or is being drawn for somebody else.
The first clause is straightforward: while one hand is engaged in filling the jar, the other hand is engaged in labor, and the labor spoils the drawing. The remaining clauses teach something less obvious. Drawing water for the chatas is itself reckoned as a melachah, so when a person fills two jars at once, each act of filling counts as a melachah with respect to the other, and both are invalidated.
Notice how this dovetails with the ruling that a person who performs the kidush on another man's water does not disqualify that water through his melachah, since it is not his. One might have thought that the same leniency would apply to drawing: that if a man draws water on behalf of somebody else, his labor should not disqualify it. The Mishnah teaches otherwise. The act of drawing invalidates the other drawing regardless, bein lo bein le'acher, whether he is drawing for himself or for another.
This explanation follows the approach of the Rambam, who holds that filling the jar is itself classified as a melachah. The Raavad, however, writes that in his view the disqualification here does not stem from melachah at all, but from hesech hadaas, a lapse of attention. Attentiveness is the underlying reason that melachah spoils the water in the first place, and it is by this criterion that the disqualification is defined. A person cannot direct his mind to two matters at once, and so drawing two jars simultaneously necessarily means his attention is divided.
The difference between the two approaches is real. According to the Rambam, melachah invalidates the water in its own right, even in a case where the person's attention was never diverted from it. According to the Raavad, what stands behind our Mishnah is the impossibility of concentrating on two things at the same time. Two paths to the same halachah: the first that of the Rambam, the second that of the Raavad.
Either way, the practical lesson of the Mishnah is clear. The water of the chatas demands the undivided involvement of the one drawing it. Two jars filled at once, or one hand filling while the other works, cannot yield fit water, and this is so whether the water is his own or drawn for the sake of another.