My father was what our friends across the pond call a barrister. He tried cases for forty plus years in the Commonwealth of Pennsylvania. He almost never lost his temper. He taught us carefully that if you do lose your temper, you can't think clearly, and you are almost certain to say the wrong thing.
It's an old lawyer's trick to make a witness angry, in the hope that he'll say something he wasn't supposed to. (Allegheny County Coroner Cyril Wecht falls for it every time.)
To win an argument, keep your temper, stick to your guns, and don't back down. It isn't easy, but it works every time.
Dad used to line up his points like bowling balls, and grin like a fool as we knocked them down.