Sometimes anxiety is the rational response. If you are in a dangerous situation, then anxiety is protective. The problem comes when anxiety is a response to situations where there is no danger.

You can find yourself feeling anxious if you are in an unbalanced relationship.
  • Do you find it hard getting air time to express your opinion?
  • Do you feel that compliance is the easiest option?
  • Do they have to have the last say in everything?
  • Is their information always so much better than yours?
  • Do they pout and shout until you give in to them?
  • Are they highly sociable and charming with strangers?
Some people need to feel in control and won't compromise for fear of losing control, without which things might fall apart. The easy option is just to submit and comply. But that just fuels resentment and anger. It is fine for someone to want to control their own life. It is not fine to spread that need for control onto others around them. Your habitual compliance empowers them but at the cost of your own self-esteem. Well, what to do?

Focus on your breathing and relax. This will help them feel less tense too, so they can quieten down.
Don't engage.  Getting upset is just fuel to the fire.
Ask exploratory questions. Get them to expand on their point of view. Restate in different words what they said. You don't have to act on this knowledge. The moment will pass. Keep your voice quiet and slow. Nod a lot.
How are you feeling? Notice your emotions. Knowingly or not, he or she is trying to trigger this response. Being aware, next time you can actively avoid these emotional responses.