One of my favorite Church Fathers to read is St. John of Damascus. He is a saint and one of three dozen Doctors of the Church, which means that his writings are held in very high regard. He was an Arab born in Damascus in 675 and he became a monk in the Mar Saba monastery in the Holy Land. He was ordained a priest in the last years of his life. He is known for his writings on theology and polemics against heretical movements. St. john is also known for his extensive writings on the Assumption of Mary and is referred to as the Doctor of the Assumption. He died in 750.
St. John was also one of the first Christians to write a polemic against Islam. This polemic gives us an opportunity to engage Islam in dialogue and to expose the double standards often used by Islamic apologists. This tactic is best used when there is long term dialogue. This cannot be done over one discussion.
This dialogue starts with a recommendation. Find a Muslim that you know and recommend that he read St. John’s tractate on Islam. It’s only a couple of pages so it’ll be easy to convince the Muslim to read it.
When the Muslim gets back to you later on, he will probably say that the tract contains several errors and misrepresentations. At this point, don’t argue with him. Let him point out the errors. Once he points them out, accept them and admit that they’re mistakes. Even saints and Doctors of the Church can have errors in their writings.
This is where you spring the trap. Point out that just like St. John misrepresents Islam, the Quran misrepresents Christianity. Having just given you his standard for St. John, he won’t be able to pull out a new standard without being super obvious. Once he tries to pull out the new standard, this is where you need to get him.
In order to complete this argument you need to have examples of Quranic errors about Christianity. I recommend using Surah 5 and it’s misrepresentation of the Trinity by saying that Christians believe Mary is part of it. Another good examples is the Quran stating to the Jews that they believe Ezra is the Son of God just how Christians believe that Jesus is the Son of God. There are other examples you can pick but in my mind, these two are the clearest Quranic errors by far.
As Christians, we can believe that St. John made mistakes. He was simply writing a polemic, not Sacred Scripture. If you know both documents very well, you can ever argue that St. John represents Islam better than the Quran misrepresents Christianity. I certainly believe that he does.
At this point you can point out that a fallible human being(and an Idolater according to Muslims) criticizes an opposing religion better than the Quran does.
The document by St. John of Damascus can be found on this Greek Orthodox website.