The first time (and every subsequent time) he brought up this point I said yes, I could be wrong. The thing is, everyone could be wrong, if we are being honest with ourselves we have to admit this is a possibility. We are all missing some information and we can't think of everything. There are certainly logical arguments that I haven't thought of on any given topic, and it's possible that my mind could be changed. Furthermore, if I'm wrong about something, there is almost certainly evidence out there that I have either never seen or mistakenly dismissed showing that I am wrong.
I think what really bugged me about this was that he seemed to be happy when I said I might be wrong. It was like he tricked me into admitting it or something. This doesn't mean he wins, it just means I'm accepting an essential truth which he is refusing to do. Furthermore, I would argue that since I am open to being wrong and changing my opinion, and since I accept that I might have made a mistake in the past and am willing to refine my positions, I have a much better chance of being correct than him. Admitting that you don't know something really is a path toward truth, asserting that you Know the Truth is not. I could be wrong and I'm fine with it. Actually, I'm proud to admit this fact. Being comfortable with "I don't know" and being willing to alter your positions is a virtue.