Exactly. For all you know that's a costume and his shooting your pet is the opening move of an armed and hostile home invasion.
There is a loaded AR within arms reach of me as I type this - with a mix of ball, HP, and LAP rounds in it. If I heard gunfire in the back yard I'd use it. If the person was lucky they would be facing away from me when I engaged - I might, might give them one chance to drop their weapon. However, if I were in their line of fire and/or they refused to obey commands immediately ... shoot center mass until you run dry or the target is down.
And all my bullets have glossy little black tips on them just in case the threat has a "tough hide".