Nothing you say will be convincing enough to settle the argument, and an argumentative person will likely not admit it even if they are wrong. Save yourself a headache and just say you're not going to debate the topic.
[header] How to annoy argumentative people [title] Don't argue. [step] It can seem difficult to avoid being drawn into a debate. When faced with a very argumentative person, it is important to remind yourself that your antagonist does not likely want to hear your opinion.