You're bound to reach an impasse in an argument once in awhile. When you do, stop talking. Your chances of working anything out when you are both upset is very close to zero. Don't waste your time. Don't risk saying or doing anything more you'll regret. Go off by yourself and do the following:
Do something that will calm you down physically. First distract your mind. Get your mind off the situation. Watch a movie, read an engaging book, surf the internet, play a game. The second stage, once you've gotten yourself out of the soup long enough to think straight, is to deeply relax: Meditate. Soak in a hot tub. Take a hot shower. Listen to relaxing music. Get as deeply relaxed as you can.
Do not decide anything. Draw no conclusions. The more upset you are, the more distorted your point of view will be. So any decisions you make are more likely to be bad ones than good ones. People just aren't as rational and don't think as clearly when they are upset. It's not just you, it's all of us. So don't make any decisions or come to any conclusions when you are mad.
Then think. Think about what you were arguing about. If you get upset again, calm down again before you try to think. When you're done thinking, consider talking to your mate about it. Sometimes there will be nothing to talk about because the fight was really about nothing important. You just took something wrong (or she did) and it created a kind of reverberating feedback loop that escalated into an impasse.
When a microphone gets too close to its speaker, it creates a feedback signal that gets louder and louder. All you have to do is move the microphone away from the speaker. You don't need to fix anything. Nothing is wrong. All that happened was a feedback loop got started and you have to separate the two. Sometimes that is true of you and your mate. You'll figure that out once you can calm down and think about it.
But if there is something you two need to talk about, think about how you will approach the subject. When you've got it worked out, then go find your mate and talk about it. This is the sanest way to bypass an impasse.
Adam Khan is the author of Principles For Personal Growth, Direct Your Mind, and co-author with Klassy Evans of How to Change the Way You Look at Things (in Plain English). Follow his podcast, The Adam Bomb.