The easiest way out is the way out, and of course you only take it when there really is no other way. Because actually your job is super fun, right? So let’s first try to settle this feud. You must have thought of that yourself, but HOW? We can help you with that.
Think about what you want to achieve. Do you agree to disagree? Will you accept each other’s points of view? Is it really your goal to improve the relationship or do you just want to get even?

Always put your arguments and desires on paper first.
Then your emotions won’t come out immediately during the conversation. Some people think it’s dull, but it helps to practice the conversation with someone completely blank facing both of you. Your preparation is crucial, try to think of concrete situations that support your point of view and wishes and try to determine what you think the conflict is about.

Then comes the hardest part: listening!
It can relieve a lot of tension when you listen to the other person and show that you understand his or her point of view. Think of some open questions to ask your supervisor in advance. Put these on paper as well. The purpose of these is to check whether your supervisor does indeed have the opinion you attribute to him or her. Then you can ask further questions. So first try to get as clear, unbiased a view of your supervisor’s point of view as possible. Then you can state what you think about it. That makes it more tangible for the manager.

Golden Rule
Make sure they are facts, though. Never come up with things you learned through someone else! If you don’t come out of such a conversation right away, don’t despair; there are more roads that lead to Rome. We know almost all of them.