It's a whole bunch more complicated than that - I'd highly recommend the Radiolab episode
Post No Evil and the documentary
The Cleaners for the full story.
Facebook doesn't have a blanket policy of removing violent content, for wholly legitimate reasons. Many users in Mexico very strongly want videos of cartel murders to stay on the site, because they feel that they are important reportage of something that the mainstream media is unwilling or unable to report. Many users in Syria very strongly want videos of IS murders to remain on the site, because they want the world to see the suffering that IS has wrought on their country.
If Facebook just delete all violent content, they're robbing the victims of violence of their voice - it doesn't feel like Facebook are protecting users of their platform, it feels like Facebook are complicit in covering up the crimes of drug cartels and terrorists.
It's not enough to identify that a video is violent - they need to know context. Is this particular video in this particular context a cry for help or a celebration of evil? Will removing this video silence the propaganda of a murderer, or will it help to conceal their crimes? Does this video show the death of an unidentifiable person in an ungoverned warzone, or is it vital evidence that urgently needs to be forwarded to the relevant authorities? For now, only well-trained human beings are capable of making that call.
This sort of dilemma points to the fundamental impossibility of moderating Facebook to the satisfaction of everyone. Some users complain about pornography, so Facebook make a policy to take down the porn. Other users complain that these policies are sexist and protest outside Facebook's offices to free the nipple. Facebook end up with several pages of rules that allow their army of moderators to consistently distinguish between pornographic and empowering nipples, but nobody's really happy with the outcome.
Facebook are doing a really crappy job of looking after their moderators, but that issue is fixable if we apply enough pressure. There are many other problems with moderating Facebook that are far less tractable and have far wider consequences.