I think it's great you have that level of confidence in yourself. Personally, I tend to back down when the other person starts talking in a particulat tone, indicating they really believe they're right, (this normally happens when discussing something that is fact, eg: the difference between our term dates and normal students term dates) because I don't have faith in myself that I'm right. (As it turned out, several times I was right, but thats kinda irrelevent after the conversation)