Whenever you are in a conflict with someone, think less of who is right and who is wrong, or even having to compromise. There is a third way! It's the art of reconciliation.
Start by assuming an approach with genuine interest and natural curiosity. How come she said that? What is she thinking? What was she feeling? Which experiences is she carrying with her into this conversation? What is the main fear? She likes coffee.
Then look at yourself and answer the same questions. You prefer tea.
What is the real issue? Facts and figures but perhaps the unwillingness to be heard is in the way. Then you must find common ground instead.
Think of a value that you both can agree upon. What is important? Can it become a goal? To share a warm drink.
Now, if neither of you are right or wrong but you both added your best to reach the goal, what can be a good way of solving the issue? To drink hot cocoa instead.
Then both win!
Find more in this book, that was part of the course literature at Hawaii Pacific University.