English Explanation of Mishnah Eduyot 3:12

Rabbi Eleazar ben Azariah allows three things and the Sages forbid them:
His cow used to go out with the strap which she had between her horns;
One may curry cattle on a festival;
And one may grind pepper in its own mill.
Rabbi Judah says: one may not curry cattle on a festival, because it may cause a wound, but one may comb them.
But the Sages say: one may not curry them, and one may not even comb them.
Mishnah twelve contains three cases where Rabbi Elazar ben Azaryah was more lenient than the other Sages.
Section one: It is forbidden to carry things in the public domain on the Sabbath. This is true even for a person’s animal, since it is forbidden to make one’s animal perform work on the Sabbath. Rabbi Eleazar ben Azariah allowed his cow to go out with a strap between its horns, since this strap was only an adornment and therefore he did not consider it “work”. In the same way a person can wear clothing in the public domain and that is not considered carrying. However, the Sages forbid cows from carrying anything, since most cows do not do so. Furthermore, if others were to see this they would think that it is permitted for an animal to work on the Sabbath.
Section two: Rabbi Eleazar permits a person to curry an animal on the festival, even though that might cause a wound. Currying is a type of combing done with a sharp metal comb. Rabbi Eleazar permits this activity since even if he causes a wound he did not intend to do so and unintentionally performed work is permitted on the Sabbath. In section four, Rabbi Judah states that currying is forbidden since it will cause a wound, but combing with a wooden comb is permitted since it will not cause a wound. In section five the Sages state that even combing is forbidden, lest by permitting combing one might assume that currying is also permitted.
Section three: Rabbi Eleazar ben Azariah permits the grinding of peppercorns on the Sabbath, even in grinders made for grinding large quantities of peppercorns. Although this is a large amount of work, and it is clear that most of the pepper will not be used on that day, Rabbi Eleazar nevertheless permits. The Sages forbid this. According to them, one may grind peppercorns only in small quantities with a mortar and pestle, since grinding more than this would be allowing one to prepare food on the festival for a week day, which is forbidden.