The ruling on feeding in the expiation for killing

The answer – and Allah is the One who grants success – is that the scholars of the madhhab have said: whoever is unable to free a slave and fast does not switch to feeding or clothing, because they are not mentioned in the verse.
I say: Allah, exalted is He, has made feeding a substitute for fasting when it is impossible, in the expiation for ẓihār and in the fast of Ramaḍān, and in some cases He has given a choice between fasting and feeding. It is therefore possible to analogically relate this fast to the fast of Ramaḍān and the fast of the expiation for ẓihār.
Perhaps Allah, exalted is He, did not mention feeding in the expiation for killing because it is already known and established in the Sharīʿah that fasting, when it is impossible, has as its substitute feeding one poor person for each day.
If it is said: Analogy and attachment are not possible here, because: in the expiation for ẓihār and in the fast of Ramaḍān, the substitute for each day of fasting is feeding one poor person; in the expiation for an oath, feeding ten poor persons correspond to fasting three days; in the fidyah (compensation), feeding six poor persons correspond to fasting three days; in the expiation for hunting (game while in iḥrām), it is not specified, rather Allah, exalted is He, says: “…or its equivalent in fasting” [al-Māʾidah:95]; in tamattuʿ (the combined ʿUmrah and Ḥajj), fasting ten days is set against offering a sacrifice. In short, the foundational patterns are different.
We say: We have attached (this case) to the fast of Ramaḍān and the fast of the expiation for ẓihār because it most closely resembles these two foundational cases, as is not hidden.
Analogy (qiyās) is an evidentiary method recognized in the Sharīʿah, and its effective cause (ʿillah) is known by textual evidence: namely, inability to fast, as indicated in His saying, exalted is He, regarding the expiation for ẓihār: “And he who is unable – then (his atonement is) the feeding of sixty poor persons.” [al-Mujādilah:4]

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2