For a start, killing a dog violently is not self-defense. It is not necessary. Perhaps injuring the dog enough for it to back off is a necessity, but actually killing it and violently is only showing the person had no respect for animals or life. Try to imagine the scenario. The dog comes and perhaps begins attacking the man, the man hits the dog in self-defense or kicks it. If the dog comes back for more, he does it again. This should be enough to get rid of the dog, but killing violently, it implies the person reacted in self-defense and then some, and then a lot more. Though it is not clear exactly what happened.
I say honest self defense because I've met people, such as my mailman, who are afraid of my dog and have gotten terribly close to striking my dog just for my dog walking up to them. I'm not against any human killing any animal as long as their life was in danger. Now, a dog isn't as easy to put down as a person, I would assume that's why it was "violently". If it was violently because the person went overboard and perhaps didn't even have to end the life of the animal, then it's a different story. I would still say that no, the person shouldn't end in jail, but a hefty fine should be paid to the owner of the dog and psychological help should be forced with a great deal of community service. But if it was violently like some people that leave 'em out to die or was tortured? I wouldn't be opposed to having the same treatment done to the person. I love my animals and if some sick person deliberately went overboard, I'd most likely help my dog out and whoop the guy and seek the heaviest weight that the law of justice has. This being said, what's with the odd topic of the opinion? Did someone get put in jail recently for killing a dog?
If the dog was killed in actual self defense, and the life of the individual who killed the dog would otherwise have been in serious jeopardy, then it's simply not right to imprison them for defending their own life. How 'violent' they or others may find the specific incident to be is totally beside the point; if he didn't defend himself, he would likely be dead, or at least seriously injured, and the dog would have been put down regardless.
If the dog is using violence then it stands to reason a person should be able to do the same.
I person who kills a violent dog is a hero in my eyes. What it it had been a small child that couldn't defend themselves? If a person went out of their way torture the dog that attacked them then perhaps their is a case for criminal investigation. However it's hard to feel sorry for a dangerous dog.