That Obama clip is somewhat popular with libertarian types, accompanied with some form of, "See! Aha! He's admitting it!". As a "libertarian type" myself (though I try not to use that word to describe myself since it has a muddled meaning), my reaction is more along the lines of, "Well, yea."
[1] https://en.wikipedia.org/wiki/State_(polity) [2] https://en.wikipedia.org/wiki/Government [3] https://en.wikipedia.org/wiki/Monopoly_on_violence [4] https://www.youtube.com/watch?v=kpITpm5NxOE&t=1m54s (not endorsing the source) [5] https://www.youtube.com/watch?v=kpITpm5NxOE&t=1m35s (more context)
[1] https://en.wikipedia.org/wiki/State_(polity)
[2] https://en.wikipedia.org/wiki/Government
[3] https://en.wikipedia.org/wiki/Monopoly_on_violence
[4] https://www.youtube.com/watch?v=kpITpm5NxOE&t=1m54s (not endorsing the source)
[5] https://www.youtube.com/watch?v=kpITpm5NxOE&t=1m35s (more context)
The state, with due process and a mandatory trial by your peers, is really the only thing worth entrusting with a right to violence.
It certainly isn't perfect, but at least we control it, and it works mostly in our collective best interest.