I have a non Christian friend with whom I discuss religion. This has widened my knowledge about my faith a lot; because I had to ask and study in order to answer his questions. Generally speaking, do you think it is worth the while to argue about and discuss religious matters?
Evangelizing is a commandment in the Holy Bible. It is our duty as Christians to spread the Word of God whenever we get an opportunity to do so. If your friend is interested to know about Christianity and not just ask questions for the sake of arguing, you should encourage him to ask and try to answer him. In a way you are learning more about your own religion and at the same time, by answering his questions, you are correcting the misconceptions he has with the hope that our Lord will open his eyes that he might see the truth and believe. But if it is just for the sake of arguing, I do not recommend your continuing with these discussions because they are pointless.
Meanwhile you need to study your Holy Bible and get to know the Lord more.