Koah de-Heteira Adif
Ḥullin 58a (original, English trans.) is one of the places in the Talmud where the phrase כח דהיתרא עדיף (“the strength of the lenient ruling is preferable”) appears. Many people are familiar with the use of the phrase in post-Talmudic literature, where it signifies the preference to rule leniently in questions of law.
What some may not know is that its original meaning in Talmudic literature is quite different. Eliav Schochetman wrote the following:
The dictum, “koaḥ dehetera adif“, appears six times in the Talmud, always bearing the same meaning. The redactors of the Mishnah and the Baraita preferred to record a case that illustrates the entire logical scope of the application of a permitting principle of a particlar tanna on the assumption that the tanna would have used this principle to permit in the case under discussion. This was as opposed to recording a case that illustrated the consequences of the adoption of the prohibiting principle of a particular tanna on the assumption that the same tanna, upon applying the prohibiting principle, would also have prohibited in that case.
In other words, in the Talmud the phrase is not use in order to choose the more lenient opinion instead of a stricter opinion, rather, it is used as a literary device to emphasize the difference of opinions between two sages in a particular case. One can easily prohibit something, but if one wants to permit something, there is a reason for his reasoning to be brought. Again Schochetman:
The Talmudic context of the principle does not relate to the authority of the posek to rely upon halakhic considerations as a source for permitting, but rather, relates to a principle governing the redacting of the Mishnah and the Baraita.
Source: Eliav Schochetman, “The Power to Render a Lenient Ruling: “Koah Dehetera Adif”,” in Jewish Law Association Studies VI The Jerusalem 1990 Conference Volume (1992): 125-55. A Hebrew version is found in Maḥnayyim, vol. 5, 1993, 72-89.