The problem he identifies between the two sets of data is that those in favor of gun control only look at numbers for gun deaths, while he looks at the numbers for violent crimes. The gun death numbers include suicides and police shootings, neither of which provide any reason for banning guns in my mind.
One of the rationales for carrying a weapon is to prevent crimes such as burglary, rape, assault, and robbery. Your video provides evidence
indicating that banning guns does not reduce violent crime, and may very well increase it. (By the way, Australia showed a similar jump in violent
crimes after their gun ban.)
If three guys come at me with tire irons swinging, I would rather there be three gun deaths than one assault and robbery resulting in extended
hospitalization or death.
To be honest, I don't see the gun ban as a useful solution to violent crime.