It was a very important issue because it essentially defined the power of the Caliph compared to the Ulama (clergy). If the Quran was uncreated, it meant that the word of God was absolute in its writing, and after interpretation by Ulama could not be questioned by the more customary rule of the Caliph. On the other hand if the Quran was recognised as created by man, the Caliph could have his own interpretation and sometimes overrule the decisions of the Ulama.

As people have said, it's actually more complicated than this (and my memory was a bit hazy). The Qur'an was seen by both sides as the word of God. It was therefore infallible in terms of text; nobody was questioning how it was written or by whom. If it was "created", it meant the Qur'an would be specific to a time and place; the arrival of the Prophet and the beginning of Islamic civilization. By rooting it in a time and place, that would mean the meaning (in terms of its application) might change more as time goes on and societies changed. It would mean the word of God would be applied in different ways.

On the other hand if it was "uncreated," it would be eternal and relevant to all societies in the same way, with far less interpretation. This disagreement was mainly academic until the Mihna (848/51AD), a sort of small-scale inquisition, when it became an extremely contentious issue as the Caliph al-Ma'mun realized uncreatedness would mean less interpretation and therefore his supposedly divine rule would be restricted by religious text and the Ulema (clergy). The Caliph managed to define religious, legal and political roles during the Mihna, which was helpful in that he wasn't so much competing so frequently for various kinds of power, but he failed at establishing the createdness of the Qur'an. To this day it is generally seen as uncreated.

Source; Hugh Kennedy, The Prophet and the Age of the Caliphates

Edit: To the point of philosophers being divided, the popular opinion of the "Rationalists" at this time was that the Quran was created. The "Traditionalists" believed it was coeternal with God because it was God's literal word and God himself is eternal. It seems that sometime during the reign of the Abassid Caliph al-Mu'tasim (842-ish), popular opinion shifted from Traditionalist to Rationalist; probably simply to gain favor with the courts, be allowed to continue teaching and avoid flogging or worse. The reason for which u/jamez042 has already posted.

Source: chapter 6 of No god but God: The Origins, Evolution, and Future of Islam by Reza Aslan

Yes, this debate occurred in Muslim Antiquity, with the position that the Qur'an was uncreated eventually winning out. What you, and others who have answered your question, might now know is that there is a specific sect, the Ibadis, that still upholds the idea of a created Qur'an. Ibadis (who comprise the majority of Muslims in the Sultanate of Oman) believe that the Qur'an as it exists is a created object separate from God's eternal speech.

Why is this such an issue? Ibadis believe this because in their interpretation an uncreated, eternal Qur'an breaks the towheed, or oneness of God: since God is the single eternal, uncreated being there cannot be anything else eternal with him. God's eternal speech is one of his attributes, and isn't separate from him, but the Qur'an is manifestation of God's speech separate from him and therefore created.

To answer the second part of your question, I can't elaborate since I know relatively little about Christianity, but I think that an analogous debate occurred among European thinkers who argued whether or not Christ was co-eternal with God before he was incarnated.

On Ibadism: Valerie Hoffman, The Essentials of Ibadi Islam, Syracuse University Press, 2012 is probably the best text on issues of Ibadi theology.

In regards to parallels in Christianity and Greek philosophy:

The 4th century did see a fairly vigorous debate over the nature of the relation between God and Christ, and what "god" mean when applied to Christ, and whether he was co-eternal with God the Father. The point of parallel would be specifically in the designation of Christ as "the Word" (Logos), and its interactions with 2nd century theology that used this as a primary category for understanding that relationship.

I'm well equipped and happy to discuss the above, but I am unaware whether this really had any impact on the Islamic debate you are discussing.

I'm not aware of any parallel discussion in Classical Greek philosophy, as the question of uncreatedness seems to be a philosophical issue that primarily arises in monotheistic contexts. It's a very interesting debate within Christianity, and I can see how it would be important within Islam.

The idea that the Qur'an was created was developed by a group called the Mu'tazilites, a sect created by a man called Wasil ibn Ata.

Wasil ibn Ata was a pupil of classical scholar Hassan alBasri, but left him over an argument about the fate of Muslims who commit major sins. Wasil opined that the Muslim who dies without repenting for such acts abides in Hell forever. Al-Basri maintained the sunni belief that it was up to God to decide whether or not to forgive (or punish). Wasil then detached himself from Hassan alBasri and decided to teach his own views. Hassan alBasri said "I’tazalna Wasil" (trans. "Wasil detached from us"). Thus, from then on, Wasil and his group were called Al-Mu'tazila (a derivative of i'tazal).

Some people are hard hearted and become extreme because they never seek knowledge outside their comfort zone (see Khawarij). The Mu'tazilite sect rode the opposite end, absorbing many foreign sources but not always filtering them. They claimed to be upholders of reason and logic (even when it contradicted reason and logic...). The following 3 are their pioneers:

• Qadi Abdul Jabbar: from Yemen. Put all Mu’tazilite ideas in book called Al-Mughni.

• Sharif Al-Murtada: Head of Shia in Baghdad. A man of literature, but not a philosopher. Noted for reconciling Mu'tazilites creed by using language to explain differences w/ traditional Sunni beliefs.

• Al-Zamakhshari: Lived in Mecca for long time. Combined philosophy and language. His contribution was popularizing Mu’tazila thought. Noted for his eloquence, but was very harsh against scholars who disagreed with him.

side note: All the work of these 3 began to crumble when the polymath Imam Fakhr alDin alRazi released his seminal work, alTafsir alKabir, but that's for another time...

The Mu'tazilites carry 5 main principles. The one that concerns your question is their belief regarding Tawheed aka Oneness of God. Like the Sunnis, they believe in absolute Oneness of God, but unlike the Sunnis, they differ on God's attributes. The Sunnis believe that God has 99 attributes that simply describe God's characteristics. The Mu'tazilites rejected the 99 attributes notion, because to them, it created a sense of multiple beings. For example, God is called Al-Rahim (the Most Compassionate) in the Qur'an. Since human beings can experience compassion for each other, they saw this as a contrast (and eventually a possible partnership) between man and God. The Sunnis thought that was a ridiculously paranoid.

What I've written so far is merely background, all in the hope that the following quote (via Dr. Muhammad `Imarah) makes sense to you:

The people who spread the idea of the creation of the Qur'an based their opinion on the nullification of the idea of having more than one eternal being. This first started when they argued with the Christians who tried to manipulate the statement that Allah is Supreme Eternal by saying: If it is true that Allah is the Supreme Eternal, and so are His words, and in the Qur’an, Jesus is described as “Allah’s Words”, hence, Jesus himself is also eternal, so he is lord and the son of Lord.

For Mutazilites to refute this idea, they nullified the idea that Allah’s Words are eternal; in fact, they maintained that these words are part of Allah’s creation. The Mutazilites did this with aim of closing the door to any pretext which might be taken by others to claim that there are many eternal beings.

p.s. edited for perpetual grammatical errors.

p.p.s. I link to Wikipedia to give you a faint idea of who these people are. I do this out of practicality but please be aware that it's an extremely flawed source, especially when it comes to anything semi-controversial.