The dog's last lunge toward the officer who killed it was very fast and aggressive, and the officer had just a split second to react. He probably just reacted on a fight-or-flight instinct, and unfortunately, in this instance, it ended with lethal force.
If I was in the same situation at that split second, I might have done the same thing. I was once chased and attacked by an aggressive dog before, and I rank it as one of the most terrifying experiences in my life. Being attacked by an animal with clear intent to harm or even kill you is just so primally scary that there's no way to think and react rationally - you just do whatever you can to get away and survive.
It's a pretty crappy situation all around, and I feel terrible for the owner of the dog. I still blame the officers for initiating the situation, but I do understand why the officer reacted the way he did.