My wife has no problems with guns, but loves animals. Still, in the situation that the OP describes, I'm sure that she'd be among the first to say that if an animal displays the attitude that the OP described, and threatened any human being with that type of aggression, that person should be allowed to defend him/herself by any means available, even if it meant using a healthy dose of napalm.
I hate to see animals abused or mistreated. But, I won't draw a line at any form of effective deterrent at my disposal, lethal or otherwise, if they threaten myself or any member of my family. I see no alternative to this mindset.
Frankly, I'd be insulted and demoralized should my wife tell me that my life and safety are worth less than injuring an animal who wished to rip my throat out and leave me lying dead in my own yard.