Read your state laws.
If a person is in fear of “great bodily harm” from an attacker they are justified in using deadly force to prevent that. Most state statues read such as this example:
“Great bodily harm” means bodily injury which creates a probability of death, or which causes significant serious permanent disfigurement, or which causes a significant permanent loss or impairment of the function of any bodily part or organ;
Great Bodily Harm”
“The term `great bodily harm’ as used in statute stating when an assault and battery becomes aggravated, is not susceptible of precise definition, but implies an injury of a graver and more serious character than ordinary battery. Herrington v. State, 352 P.2d 931, 933 (Okla. Cir.).”(15)
“Great bodily harm” means bodily injury which creates a substantial risk of death, or which causes serious permanent disfigurement, or which causes a permanent or protracted loss or impairment of the function of any bodily member or organ or other serious bodily injury.”(16)
See:
http://www.cnn.com/interactive/2012/04/us/table.selfdefense.laws/
It was up to the cops who arrested him to know their state laws on displaying/brandishing a weapon.