i wont shoot a dog even if they ruin a hunt.....i have a dog and my sister has 2 and we cant keep collars on any of them they all pull them off. They run our family land and im sure they occasionally get on the neighbors land also. I know they have chased deer before. I look at it like they are doing the EXACT same thing you are and theirs is just pure instinct. Most dogs are all show and no fight but if a dog felt like pushing the fight enough i have no problem putting it down either. I just find it kind of amazing that so many people are so quick to shoot an animal just because it could possibly ruin a recreational activity of theirs.
All of this.