The Talmud, in discussing the view of R. Yehudah that the destruction of Chametz can only be done through burning, notes that consequently it cannot be done on Yom Tov. As Rashi explains, were it not for R. Yehudah’s limitations, other methods of removal, such as feeding the chametz to the dogs or throwing it into the ocean, could be used, without violating the prohibition of melakhah on Yom Tov.

The Pnei Yehoshua questions this assumption, citing Rashi’s comments to Beitzah (27b), concerning the destruction of challah that has become impure. There it is assumed that all methods of removal are impossible on Yom Tov, in that the pasuk (Vayikra 7:19) states: “And the flesh that touches any unclean thing shall not be eaten; it shall be burnt with fire”; any removal of the substance is equated with a meaningful burning incompatible with Yom Tov. If so, the same would seem to apply to chametz; any form of destruction should be equated with burning and should be impossible on Yom Tov (according to R. Yehudah).

The Noda B’Yehudah (I, O.C. 15) explains that there is a very significant difference between the destruction of chametz and that of impure kodshim. The latter is a goal in and of itself, and thus not attached to any particular owner; any individual who accomplishes the task has fulfilled a mitzvah, which is thus inherently significant and called a melakhah. Destroying chametz, however, is solely the responsibility of the owner, with no obligation falling on anybody else. Therefore, as only the owner’s performance would be defined as a significant act constituting a melakhah, and it does not make sense to distinguish between different individuals doing the same action, destroying chametz is only a melakhah if the method itself is a melakhah.

The Resp. Binyan Shlomo (I, 30), however, questions the premise of the Noda B’Yehudah, noting the statement of the Talmud (Bava Kama 98b) concerning chametz, that “all are commanded to destroy it”. The Resp. L’Horot Natan (XII, 19) defends the Noda B’Yehudah, explaining that the Talmud did not intend to place the obligation of destroying an individual’s chametz upon the entire population. Rather, the reference here to influencing another to fulfill his individual responsibility. The full context of the passage in Bava Kama is that one is not obligated to make restitution for chametz that was stolen before Pesach and then destroyed on Pesach by a third party, because “all are commanded to destroy it”. This reflects the fact that all are responsible for encouraging the individual to perform his duty of destroying his chametz. Destroying impure kodshim, by contrast, is not the responsibility of a specific individual.