I have seen over the years that many debates do not result in the Khawarij backing down nor sincerely accepting the evidences. Sometimes they may but on the whole they just have too much arrogance. The biggest problem is that they do not have clearly developed Usool on most subjects, furthermore they do not have clear definitions on subject matters. This creates a very difficult dilemma when debating them as they shift from one argument to the next, mix up things, create confusion etc. etc. for us as Sunni's each matter has been subjected to an Usool to derive a ruling and we are clear on definitions of various things. If you want to debate this guy, ask that he submit his definition on the topics like Hazir Nazir and Ilme Ghaib and how he defines them according to the leading Scholars. After all you can't make up your own definitions without being backed by the Ulema.