Chapter 1, Mishnah 4. In the previous mishnah we learned that we take a security deposit from someone who does not give the half shekel willingly, but we do not take a security deposit from the kohanim, out of respect for the kohanim. Our mishnah brings two opinions on a more basic question: are the kohanim obligated in the half shekel at all?
Introduction: Mixing private money into public funds:
The purpose of collecting the half shekel is that every single person should have a share in the communal offerings. For that reason, giving more than the fixed amount can create a problem: private money becomes mixed into the public funds, and the offering is no longer a fully communal offering but one that contains the money of an individual. This issue comes up first in the words of Rabbi Yehudah in our mishnah.
The testimony of Ben Buchri:
Rabbi Yehudah said: "He'id Ben Buchri b'Yavneh: kol kohen sheshokel eino chotei" - Ben Buchri testified in Yavneh: any kohen who gives the shekel is not doing anything improper. In Ben Buchri's view the kohen is not obligated to give the half shekel, and even so there is no concern about private money becoming mixed into public funds, because the kohen hands over his shekel to the community as a complete and entirely free gift, and it becomes part of the public funds. Therefore there is no problem with it, even though the kohanim are not obligated.
The response of Rabban Yochanan ben Zakkai:
Rabban Yochanan ben Zakkai answered him with exactly the opposite position: "Lo chi, ela kol kohen she'eino shokel chotei" - not so; rather, any kohen who does not give the shekel is sinning. The kohen is obligated to give the half shekel like every other Jew. At the same time, he notes that the view that the kohen is exempt does have a source, but it is a mistaken one: "Ela shehakohanim dorshim mikra zeh l'atzman" - the kohanim expound this verse to their own advantage.
What is that verse? "V'chol minchas kohen kalil tihyeh lo sei'achel" - and every meal offering of a kohen shall be entirely burned, it shall not be eaten. With most meal offerings the kohen takes a handful and burns it on the altar, and the rest is eaten by the kohanim; but the meal offering of a kohen is burned completely on the altar and may not be eaten.
From here the kohanim argued: "Vahalo ha'omer ushtei halechem v'lechem hapanim shelanu - heiach nochlem?" - but the omer, the two loaves and the showbread are ours, so how could we eat them? The omer offering is brought on the sixteenth of Nisan, the two loaves are brought on Shavuos, and the showbread is brought every Shabbos, and all of them are eaten by the kohanim. If the kohanim were to participate in the half shekel, they would have a share in the ownership of these offerings, and it would no longer be possible to eat them. On this basis they concluded that they are not obligated in the half shekel.
Rabban Yochanan ben Zakkai, however, held that this exposition cannot be made, since the law that a kohen's meal offering is burned completely was stated only regarding the meal offering of an individual kohen, his own personal offering, and not regarding a communal meal offering, and so it has no bearing on our case. He therefore ruled that the kohanim are obligated to give the half shekel.
In summary: our mishnah deals with the question of whether the kohanim are obligated in the half shekel. Ben Buchri testified in Yavneh that a kohen is exempt, and that even if he did give the shekel he is not sinning, because he hands his shekel over to the community as a complete gift. Rabban Yochanan ben Zakkai ruled that any kohen who does not give the shekel is sinning, and he rejected the exposition the kohanim made from the verse "and every meal offering of a kohen shall be entirely burned, it shall not be eaten," which was stated only regarding the offering of an individual and not regarding a communal offering.