No. It is not. That is excessive deadly force. His life was not in danger.
The only physical response warranted would have been to punch her face, at the most.
Try it in Texas.
Oooooh...! Texas! Where they shoot angry black women at the drop of a ten gallon hat.
Real tough guys.
It has nothing to do with tough guy attitude that you speak of. It has to do with respect of your fellow man. If someone is physically assaulting you and you feel that your life is endangered, you have the right to defend yourself and that includes deadly force.