The Quran (especially when read in Arabic) is a very linguistically beautiful book.

It also has to do with the fact that it is in an enigmatic meter in the Arabic language, which makes it impossible to imitate as per what Islamic scholars have studied (and even proven) over the past 1300 years, including a few notable Andalusian Iberian Islamic scholars a while ago.

The meter that the Qur'an is in can only be preserved if the exact words of the Qur'an are the same. If you change even 1 word, the meter changes, which is why it's called "inimitable." The meter cannot be used for ANY other message in Arabic language. There are other reasons for this inimitability, too, but this is probably the easiest to understand for someone who hasn't studied the subject in detail.

I am wondering if I have missed something? Do any of you have an additional reason for your beliefs?

Yes, quite a lot actually. I am glad you listed #2, however, since that is one that most non-Muslims are typically not aware of.

Another reason for belief also follows from a few things that are resultant from the fact that we know Islamic historiographical accounts are accurate (as has been corroborated by secular historians, like Karen Armstrong). Given this, we can view Islamic history as fact, not myth or fable, like some of the more far-off historical accounts of Judaism (like the Israelite migration is speculated to have been by some historians).

As a result, we can look at things like Muhammad alayhi salam (=peace be upon him) prophecizing the conquering of Constantinople, which happened about ~600 years after his death by the Ottoman Caliph Muhammad al-Faatih (fittingly named Muhammad the Victor haha).

Prophecies like this, ones that are completely unlike the open-ended "prophecies" of people like Nostradamus whom we can use as a control group to compare, are great for demonstrating the veracity of what Muhammad alayhi salam claimed and spoke of, despite the fact that he had no way of predicting such things.

Constantinople was the mightiest, most well-guarded city in the world at the time. It had survived ATILA THE HUN, who turned his ENTIRE horde of warriors around after he got a view of the city's vast walls. Yet, Muhammad alayhi salam, despite only having a handful of followers at the time, prophecized that his followers would one day conquer the city. That in itself should be stunning to any intellectually honest person:

Here's the hadith (and it's sahih, meaning authentic, and has multiple narration chains/reports):

"Lataftahanna al-Qustantiniyya wa lanima al-amiru amiruha wa lanima al-jayshu dhalika al-jaysh."

"Verily you shall conquer Constantinople. What a wonderful leader will her leader be, and what a wonderful army will that army be!"

• Ahmad, al-Musnad 14:331 #18859 [sahih chain according to Hamza al-Zayn]

• al-Hakim, al-Mustadrak 4:421-422 [sahih according to him and al-Dhahabi concurred]

• al-Tabarani, al-Mu`jam al-Kabir 2:38 #1216 [sahih chain according to al-Haythami 6:218-219]

• al-Bukhari, al-Tarikh al-Kabir 2:81 and al-Saghir 1:306 Ibn Abd al-Barr, al-Istiab 8:170 [hasan chain according to him]

• al-Suyuti, al-Jami` al-Saghir [sahih according to him]