No, he isn't. There is far more that is required by the law before it is justifiable. There must be an imminent danger of a life-threatening injury, before a "defense of self or others" claim may be made. (However, most states also allow a lethal response to rape.)
If a man pushes you for flirting with his wife (which is battery... the push, not the flirtation, LOL), that does not legally allow you to terminate his life.
That may be the black letter of the law, but I doubt that a jury here would convict someone who used a firearm to stop a man from battering a woman in an unprovoked attack in public, unless there was some extraordinary mitigating circumstance.