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.