No, arguing with him probably won't accomplish anything -- and the reason is because his problem probably isn't with his mind, but with his will. Let me explain.
During my years as an evangelist, I've often asked myself why some people resist God and want nothing to do with Him. Sometimes, I've found, their reason is intellectual -- that is, they have sincere questions or doubts about God that keep them from faith. If so, we need to answer their questions to the best of our ability. The Bible says, "Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have" (1 Peter 3:15).
But I've discovered that this isn't the problem with most people -- including, I suspect, your coworker. Instead, they don't want anything to do with God because they want to be independent and run their own lives -- and they know they can't do that if they commit themselves to Jesus. Their sins have a fierce hold on them, and they don't want to change their lifestyle or give them up.
Pray for this person, that God will break through his pride and his self-will, and convict him of his need of Christ. Pray too that your life will be a witness to him -- a witness of Christ's love and joy and peace. Remember also the Bible's injunction: "A gentle answer turns away wrath, but a harsh word stirs up anger" (Proverbs 15:1).