I tend to argue in complete calmness, perhaps with a tone of sarcasm, I'm a little over competent and egotistical at times, though I don't have much issue admitting when I'm at fault, if I'm at fault then I'll admit to it, if I'm not at fault then the person i'm arguing has little to no emotional effect upon me and if it's someone I love then I'll drop the matter as quickly as I can.
An argument need not include anger, though I guess that may just be considered an informal debate?