Chullin 19 - Shechitah - Third Outside, Third Inside, and Third Outside
If one cut one-third part of the trachea above the designated area, then his knife went downward, and he cut one-third within the designated area, and then again cut the remaining third outside the designated area, then Rav Huna says in the name of Rav that the animal is kosher, while Rav Yehudah says in the name of Rav that it is not kosher.
Why would it be kosher? Because when the animal's life departs in the middle of the cut, it departs through valid shechitah. And why would it be not kosher? Because you need the majority of the trachea cut within the designated area, and here only one-third of it was cut this way.
In the reverse case, Rav Huna and Rabbi Yehudah again disagreed, and Rav Yehudah became upset. On hearing this, Rav Huna wanted to retract his opinion, because Rav Yehudah was the direct student of Rav, while Rav Huna only heard Rav's opinion through others. Said Rav Chisda to him, "Don't retract both opinions, for they are logical, just retract that one which you did not hear directly from Rav." Thus, you will combine logic and your respect for tradition the reason for which may escape you.
Art: Henry Towneley Green - A Disagreement