We do not refer to the Qur'an in terms of 'makhluq'. We say that it is 'muHdath' (temporal/originated). If we were to call the Qur'an as 'makhluq', then there's an implication that it could be a lie or a fabrication (as Allah mentions about creation in the Qur'an). In order to understand how this debate came to be, we should look at the historical background. I have copied the below post (in quotes) from another discussion forum where this issue was raised (I am not sure if the person who posted the response was citing a scholar):
The issue of the creation of the Qur'an was not discussed during the initiate era of Islam. Rather, it was brought up in the era of the
Umayyad dynasty via the Christians who enjoyed quite a lavish
lifestyle under their rule. Sargon (I hope I translated it correctly)
was a Christian who was appointed by Mu'awiya as a high official in
the government. Sargon had a son, named "John al-Dimashqi" who
assumed the position of his father after his demise until his
resignation in the year 113 Hijri, where he devoted himself to writing
against Islam until his death in the year 160 Hijri. One of the
misconceptions that this person raised was the following:
Is (the Word of Allah) without a beginning (i'll use the word
eternal for this) or not?
If the Muslims answered:
Yes, it is without a beginning. He would reply that the Christians
belief is indeed correct, (i.e. Jesus (as) is eternal). However, if
they, on the contrary, answer no, he would say: then you claim that
the speech of Allah is created.
Now, what does John mean by this?
The answer is that when a person says that the Qur'an is created, it
implies that it is a lie and fabricated since it clearly contradicts
with the following verse:
The Messiah, Jesus son of Mary, was only a messenger of Allah, and
His word which He conveyed unto Mary, and a spirit from Him. [4:171]
The verse clearly describes Jesus (as) as "His word", so if God's
word is eternal, then Jesus is eternal, and if not, then the Qur'an is
created, meaning that it is subject to fabrication and contains lies.
We conclude that the first people to raise this issue were the
Christians, and then it spread to the Muslims and they began debating
whether the word/speech of Allah (swt) is created or not. The peak of
this debate was reached during the Abbasid era, where al-Ma'mun
adopted the view that the Qur'an was indeed created. The Mu'tazila
followed al-Ma'mun with this view, while the people of hadith rejected
it. Al-Ma'mun however, didn't find it sufficient to believe in this
theory and allow others to adopt the contrary. In fact, he forced
others to believe in it in the year 218 Hijri, whereby he gathered the
Muslims scholars and demanded that they all state that the Qur'an was
created. This was, of course, for many political reasons which I
don't see any need to discuss at this moment. Furthermore, history
records incidents of bloodshed and killings as a result of debates on
this issue. One party would issue verdicts against the other,
sometimes accusing the other sects as becoming apostates if they adopt
an opposite view regarding the creation of the Qur'an. For example,
Ahmad bin Hanbal accuses whoever believes that the Qur'an is created
is an apostate, and whoever doesn't believe that these people are
kuffar is a kafer like them.
For this reason, Ahlul-Bayt (as) asked the Shi'a to stay away from the
political dispute that this issue created, and described it as a
fitnah to cause division and lead to bloodshed between the Muslims.
The ma`Sumeen (as) (Twelver shi3ah) have maintained the emphasis on not calling the Qur'an by any name other than has been appointed for it, and they were clear in that the Qur'an is neither to be called Khaliq nor makhluq, but that it is the 'Kalam' of Allah:
4 - حدثنا أبي رحمه الله، قال: حدثنا سعد بن عبد الله، قال: حدثنا محمد بن عيسى بن عبيد اليقطيني، قال: كتب علي بن محمد بن علي بن موسى الرضا عليهم السلام إلى بعض شيعته ببغداد: بسم الله الرحمن الرحيم عصمنا الله وإياك من الفتنة فإن يفعل فقد أعظم بها نعمة (1) وإن لا يفعل فهي الهلكة، نحن نرى أن الجدال في القرآن بدعة، اشترك فيها السائل والمجيب، فيتعاطى السائل ما ليس له، ويتكلف المجيب ما ليس عليه، وليس الخالق إلا الله عز وجل، وما سواه مخلوق، والقرآن كلام الله، لا تجعل له اسما من عندك فتكون من الضالين، جعلنا الله وإياك من الذين يخشون ربهم بالغيب وهم من الساعة مشفقون.
Translation of the matn: 3Ali b. MuHammad b. 3Ali b. Musa al-RiDa (as) wrote to one of his shi`ah from Baghdad:
By the Name of Allah, the Beneficent, the Merciful. May Allah protect us and you from the fitnah, for if he does so, it is a great blessing and if he doesn't, it is destruction. We consider the argument about the Qur'an to be a bid3ah, in which the one who questions and the one who answers are partners, for the questioner is given what is not for him and the answerer is burdened with that which is not upon him [to answer regarding]. There is no Creator except Allah, `Azza wa Jall. And whatever is besides Him is created. But the Qur'an is the Speech of Allah. Do not appoint a name for it from yourself, lest you be of those gone astray. May Allah make us and you from those who fear their Lord in secret, and they are apprehensive of the Hour.
This is the view of Shaykh al-Saduq from whose book al-TawHid the above Hadith is taken:
قال مصنف هذا الكتاب: قد جاء في الكتاب أن القرآن كلام الله ووحي الله وقول الله وكتاب الله، ولم يجئ فيه أنه مخلوق، وإنما امتنعنا من إطلاق المخلوق عليه (٢) لأن المخلوق في اللغة قد يكون مكذوبا، ويقال: كلام مخلوق أي مكذوب، قال الله تبارك وتعالى: ﴿إنما تعبدون من دون الله أوثانا وتخلقون إفكا﴾ (٣) أي كذبا، وقال تعالى حكاية عن منكري التوحيد: ﴿ما سمعنا بهذا في الملة الآخرة إن هذا إلا اختلاق﴾ (4) أي افتعال وكذب، فمن زعم أن القرآن مخلوق بمعنى أنه مكذوب فقد كفر، ومن قال: إنه غير مخلوق بمعنى أنه غير مكذوب فقد صدق وقال الحق والصواب، ومن زعم أنه غير مخلوق بمعنى أنه غير محدث وغير منزل وغير محفوظ فقد أخطأ وقال غير الحق والصواب، ،
Al-Saduq said: "It has been mentioned in the Book (the Qur'an) that the Qur'an is the speech of Allah, the revelation of Allah, the saying of Allah, and the book of Allah. However, it did not contain [in it] that it is created. The reason that we refrained from describing it as 'created' is because 'the created' linguistically could mean 'fabricated/false'. It is said [linguistically], 'created/invented speech' (kalaam makhluq), meaning false/invented/lie/etc. Allah, the Blessed and Exalted says, "You only worship idols besides Allah and you create/invent falsehood"[29:17], i.e., a lie. Allah, the Exalted says: " We did not hear of this in the latter-day creed. This is nothing but a fabrication." [38:7] ('Ikhtilaaq' meaning invention and lying). Whoever claims that the Qur'an is makhluq, in the sense that it is false/a lie/invented has done kufr. Whoever claims that it [the Qur'an] is not makhluq in the sense that it is not false/invented then he has uttered the truth and said that which is Haqq and correct. Whoever claims that it [the Qur'an] is not created in the sense that it is not temporal, not revealed and not preserved, is mistaken and uttered what negates the truth and correctness."
Also, the Shaykh says:
"ومعنى ما فيه أنه غير مخلوق أي غير مكذوب ، ولا يعني به أنه غير محدث ، لانه قد قال : محدث غير مخلوق ، وغير أزلي مع الله تعالى ذكره."
The meaning of it "not being created," is that it is not false and he [the Imam] does not mean by it that it is not temporal [another way of saying created], because he (as) said: "temporal but not created, and not eternal with God, Exalted is His mention" .
If you understand Arabic, I would suggest you read the aHadith from Kitab al-TawHid, p. 223-29 under the Chapter (#30) 'The Qur'an, What is it?'.