What happens next?

How to win an argument against someone who won't lose
Stay cool-headed.
When these people are losing an argument, they tend to do little more than cut you off and then insult you. If you become irritated or enraged, they can continue to insult you as they know you are weak at that point.

Select from the following.
a). Take a moment to consider that it may come from your own experience. Usually, and always), arguments go with the punches.;
b). Instead, let these people sit down and take a walk, turn on some upbeat music, do whatever makes you feel calm and relaxed. In addition, do what you can to remain calm during the argument.;
c). If this happens, remain cool-headed but confidently move out of their way. Continue your reading and conversation and try not to engage them.;
d). Your anger can fuel their anger as well. However, when you stay rational and calm, you can continue to prove their points wrong without getting into physical violence.;
d).