GMing Makes You a Better Person: Referee
Back when I was in high school, I got a part time job as a referee for a dek/street hockey league for boys ages 10-12. In the second game I ever refereed, two boys got in a fist fight that had to be broken up by one of the coaches. I was not a good Dek Hockey referee.
Flash forward another seven years to my garage, where I'm watching four of my best friends stand up out of their folding chairs to point and yell at each other, arguing over the ethics of cursing an ogre baby to make it stronger for manual labor. I did not break up this fight either.
What we now refer to as "The Ogre Baby Incident" is a moment I often think back to when I had to actively try to stay neutral as my PC's (and players) started to participate in Player vs. Player shenanigans.
I did my duty and urged them to do all of their arguing in character which helped to dampen tensions and keep them rooted in the mindset that it's "just a game". Everyone did end up having a hilarious time, as the party was split and separated in a huff.
Since then, I've been more accustom to putting my hands up whenever players get into a disagreement and just enforcing the rules of the world. You can make suggestions as to how the players should resolve things, but ultimately it should be on them.
This is also why I don't mind evil characters in my games as long as they have a worthwhile reason or purpose. Conflict between players can be very memorable for a story if used wisely.
Impartial & Evenhanded
Over time, running an RPG drills into you the experiences of being impartial and seeing things from different views. Not only do you have to remain unbiased to your players obviously bad choices, but you also have to respond to them usually wearing the mask of someone else.
You'll grow to be better at knowing when to stay impartial and also get better at letting people make their own mistakes. Both are very valuable skills in day to day life.