Managing my own reaction to conflict/aggression

 ~ I use that emoticon because it looks to me like someone with thoughts whirling around their head... not an "angelic" person... I don't know any angels... I know some nice people but I haven't seen anyone dressed in white plucking a harp... ever! Anyway...
Yesterday I became very stressed watching a spat evolve between people I don't even know... I felt a strong compulsion to get someone "official" to stop the "fighting" ... I suspect that my "distress" is due largely to having witnessed some impressively vicious (physically, emotionally, psychologically...) arguments as a small child... 
I was pretty keen for the needless and nasty back & forth to be brought to as quick as a halt as was possible...
Both sides were not doing anything to help themselves OR the unfortunate situation... but my biggest wonder is WHY I still appeal to an "authority" figure to sort these things out... Hmmm! arghhh!
"Life Unlocked" by S. Pillay M.D. may give some insight into this...
"At the root of anger is fear"... I'm wondering if possibly in some cases if the opposite isn't also true? If the root of FEAR... is anger!! Hmmm!