What do you think if I refuse to take sides in a family fight?
It is fine if you don't take sides, being in the middle of a family feud is too stressful for most. But what exactly is going on?
I mean choosing which of the two people to agree with
You're doing the right thing by staying out of the family fight. Try to remain neutral, so that you don't damage your own relationships with your family members.
What if later on I take the side of whoever makes me madder?
Why would you choose the side that makes you madder? It would be destructive to your mental health. Just stay neutral, like I said, because you are wise enough to know that is the best option.