Two of your friends are arguing. One of them tries to get you to join his side in the argument. You say this because you don't want to choose either side.
I'm staying out of it.
This means to remain neutral. We think of an argument as a situation that you are "in" or "out of". Once you give your support to one side or the other, you are "in" the argument. If someone doesn't want you to get involved, they might tell you:
Stay out of it!
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