The goal of reading and studying the Quran together is to instill Quranic wisdom in one's heart. For this reason, the prophet peace be upon him forbade arguments and disputes regarding it.
The Prophet peace be upon him, declared in a hadith:
"Go away and leave it alone, and read the Quran as long as your hearts are one. If you disagree over it, then go." Bukhari's Sahih
According to the hadith, as long as our intentions are the same, we can get together to read and study the Quran. Study, absorb, think about, and read the wisdom of the Quran.
The purpose of these get-togethers is not to argue and quarrel, so if that starts to happen, we should end it immediately and go somewhere else. Then return the following time in unanimity with the intention of studying rather than debating.
This upholds the honor of the Quran while simultaneously demonstrating how easily that honor can be lost if we prioritize argumentation and debate over learning and comprehension.