He is asking about the reason for the difference of opinion among the scholars about saying the name of Allah at the time of slaughter

Firstly:

The scholars differed concerning the ruling on mentioning the name of Allah at the time of slaughter, and there are several views:

The Hanafis, Maalikis and Hanbalis – according to the well-known view among them – are of the view that mentioning the name of Allah at the time of slaughter is obligatory, but if it is omitted by mistake or if one forgets, then the meat is still permissible. They quoted as evidence for it being obligatory the verse in which Allah, may He be exalted, says (interpretation of the meaning):

“Eat not (O believers) of that (meat) on which Allah’s Name has not been pronounced (at the time of the slaughtering of the animal), for sure it is Fisq (a sin and disobedience of Allah)”

[al-An‘aam 6:121].

The idea that the ruling is waived in the case of forgetting is based on the general meaning of the words of the Prophet (blessings and peace of Allah be upon him): “Allah has forgiven my ummah for their mistakes and forgetfulness, and what they are forced to do.” 

Narrated by Ibn Maajah (2043); classed as saheeh by al-Albaani in Saheeh Ibn Maajah.

The Shaafa‘is were of the view – which is also mentioned in one report from Ahmad – that mentioning the name of Allah at the time of slaughter is Sunnah.

They quoted as evidence the report narrated by al-Bukhaari (5502) in which it says that a slave-woman belonging to Ka‘b ibn Maalik was tending some sheep of his in the market in al-Jubayl, near Sal‘ [a mountain in Madinah], and one sheep got injured, so she broke a stone and slaughtered the sheep with it. They told the Prophet (blessings and peace of Allah be upon him) about that and he told them to eat it.

They also quoted as evidence the fact that Allah, may He be exalted, has permitted meat slaughtered by the People of the book, as He, may He be exalted, says (interpretation of the meaning): “The food (slaughtered cattle, eatable animals, etc.) of the people of the Scripture (Jews and Christians) is lawful to you” [al-Maa’idah 5:5], and they do not mention the name of Allah at the time of slaughter.

They also quoted as evidence the report narrated by al-Bayhaqi (18890) from Ibn ‘Abbaas (may Allah be pleased with him) from the Prophet (blessings and peace of Allah be upon him) who said: “His own name is sufficient for the Muslim, and if he forgets to mention the name of Allah at the time of slaughter, let him mention the name of Allah and eat it.” But this is a da‘eef (weak) hadith; the correct view is that its isnaad ends with Ibn ‘Abbaas [and it is not to be attributed to the Prophet (blessings and peace of Allah be upon him)]. See: at-Talkhees al-Habeer (4/338)

They responded to the supporters of the first view by noting that the words of Allah (interpretation of the meaning), ““Eat not (O believers) of that (meat) on which Allah’s Name has not been pronounced (at the time of the slaughtering of the animal)” [al-An ‘aam 6:121] are to be understood as referring to that which was slaughtered for something other than Allah, as in the verse in which He says (interpretation of the meaning): “or impious (unlawful) meat (of an animal) which is slaughtered as a sacrifice for others than Allah” [al-An‘aam 6:145].

Ibn Jurayj said, quoting from ‘Ata’ concerning the words, “Eat not (O believers) of that (meat) on which Allah’s Name has not been pronounced”: This is a prohibition on meat that was slaughtered by Quraysh on behalf of the idols, and on meat slaughtered by the Magians.

The Zaahiris (literalists) were of the view that it is a condition that cannot be waived under any circumstances, not even in the case of forgetfulness, deliberate action or ignorance. This was narrated from Maalik and Ahmad, and was the view of a group among the early generations, and was the view favoured by Shaykh al-Islam Ibn Taymiyah. They quoted as evidence for that the general meaning of the verse in which Allah, may He be exalted, says (interpretation of the meaning), “Eat not (O believers) of that (meat) on which Allah’s Name has not been pronounced” [al-An‘aam 6:121], and the fact that the Prophet (blessings and peace of Allah be upon him) said: “If the blood has been caused to flow and the name of Allah has been mentioned over it, then eat.” Agreed upon.

So it is stipulated in order for the food to be permissible that the name of Allah should be mentioned, and it is well-known that if the condition is not fulfilled, then that which is conditional upon it does not come into effect. So if mentioning of Allah’s name is omitted, then the permissibility of the meat does not come into effect. This is the case with all conditions.

See: al-Mawsoo‘ah al-Fiqhiyyah (8/90); Tafseer Ibn Katheer (3/325); see also question no. 85669

Al-Qurtubi (may Allah have mercy on him) stated in his Tafseer (7/75) that there was a difference of scholarly opinion concerning that.

Secondly:

The evidence for the prohibition on eating that over which the name of Allah was not mentioned, according to those who say that doing so is obligatory or is an essential condition, is the verse in which Allah, may He be exalted, says (interpretation of the meaning): “So eat of that (meat) on which Allah’s Name has been pronounced (while slaughtering the animal), if you are believers in His Ayat (proofs, evidences, verses, lessons, signs, revelations, etc.)” [al-An‘aam 6:118], as well as the verse in which He may He be exalted, says (interpretation of the meaning), “Eat not (O believers) of that (meat) on which Allah’s Name has not been pronounced” [al-An‘aam 6:121].

Al-Qurtubi said:

So He mentioned both scenarios and clarified both rulings. The words “Eat not” indicate that it is haraam and should not be interpreted as meaning that it is makrooh. However, with regard to one who omits it by mistake or because of forgetfulness, he is not addressed here, so the condition is not binding in his case.

Tafseer al-Qurtubi (7/76)

Thirdly:

Allah, may He be glorified and exalted, did not mention that over which His name has not been mentioned among the things that He prohibited in the verses in which He says (interpretation of the meaning):

“He has forbidden you only the Maytatah (dead animals), and blood, and the flesh of swine, and that which is slaughtered as a sacrifice for others than Allah”

[al-Baqarah 2:173]

“Say (O Muhammad (blessings and peace of Allah be upon him)): I find not in that which has been inspired to me anything forbidden to be eaten by one who wishes to eat it, unless it be Maytatah (a dead animal) or blood poured forth (by slaughtering or the like), or the flesh of swine (pork, etc.) for that surely is impure, or impious (unlawful) meat (of an animal) which is slaughtered as a sacrifice for others than Allah”

[al-An‘aam 6:145]. 

But He does mention it in the verse in which He, may He be glorified and exalted, says (interpretation of the meaning):

“Eat not (O believers) of that (meat) on which Allah’s Name has not been pronounced (at the time of the slaughtering of the animal), for sure it is Fisq (a sin and disobedience of Allah)”

[al-An‘aam 6:121]

The shar‘i rulings (concerning an issue) should be worked out on the basis of all the evidence that is mentioned in the Qur’an and Sunnah, not from some of it to the exclusion of others.

This is similar to the issue of no mention being made in the Qur’an of the prohibition on all wild animals that have fangs and all birds that have talons, which is mentioned in the Sunnah, as was narrated by Muslim (1934) from Ibn ‘Abbaas who said: The Messenger of Allah (blessings and peace of Allah be upon him) forbade all wild animals that have fangs and all birds that have talons.

And Allah knows best.