Before Pesach we burn whatever chametz we have not sold or otherwise removed from our ownership. Why specifically do we burn it instead of finding another way to dispose of it? Perhaps a lest wasteful way would be to feed it to fish or other ownerless animals.
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The Mishna in Pesachim 2:1 records a dispute as to how Biur Chametz is to be done. Rabbi Yehuda, comparing the destruction of Chametz to the destruction of invalid Korbanot, rules that Chametz must be destroyed by burning. The Chachamim there argue and rule that any form of destruction (tossing into the sea, or crumbling it into the wind) is acceptable. The Rambam, a Sephardi, in Chametz U'Matza 3:11 rules like the Chachamim, while Tosfot, an Ashkenazi, on Pesachim 27b sv Ein rules like Rabbi Yehuda. The Shulchan Aruch (OC 445:1) rules like the Rambam and Chachamim, while the Rama notes that the custom in Ashkenaz is to destroy the chametz with fire, seemingly (and the Mishna Berura sk 6 notes this at well) in order to fulfill the mitzva according to Rabbi Yehuda as well.
Note that even without that custom, the Shulchan Aruch rules in OC 448:6 that you can't feed chametz to an ownerless animal based on Yerushalmi Pesachim 2:1. This would only apply after the 5th hour on Erev Pesach when benefit from chametz becomes prohibited.
Kaf Hachayim 445:11 quotes that kabbalistically it is preferable to burn the chometz as it symbolizes the destruction of the Yetzer Harah.
The Rashash (Pesachim 21b) suggests, according to one opinion, that eating chometz accomplishes burning it, since the heat of your body is like burning. And אדם כי עץ השדה, a man is like a tree, so you even get the benefit of using a wood fire, which the Rashash in Shabbos 66 says is a necessary part of burning it. However, the Rashash only suggests this approach within Rashi's understanding of the Gemara. Eating chometz in the days leading up to Pesach in order to get rid of it, in any event, would present no issues and fulfill the mitzvah of burning it according to this Rashash.