I believe that this conflict must be about yourself, and so we cannot do this. You could talk about childhood experiences, trips that you went on, etc.
It shouldn't be too hard. Hope this helps!
You could use this;
You and your best friend went to go see a movie. You wanted to see this funny movie while your friend wanted to see a romantic one. In the end, you guys ended up going to separate theaters and didn't see each other again, because of this big fight. You lost a friend that day
