The cop was actually acting rationally. Consider his position...
He knows killing the dog will not result in his suspension or termination. In fact, doing so is standard practice...
Puppycide | Cop Block
He may need to fill out a form for discharging his firearm, but in California (I think), that procedure is going away.
He knows that killing the dog will not result in a decrease in his salary and benefits. He does not need to please customers.
He knows that killing the dog will place him in good standing with his fellow officers.
He knows that killing the dog may fuel bad feelings toward cops, and make those who support cops question that support. But his actions also convey a clear message to others: "I'm am a police officer. Do what I say, or I will hurt you."
The former is temporary. Most people have been indoctrinated into thinking cops are the good guys (much like feelings toward our military). Hence, bad feelings and questioning of support tend to dissipate.
The latter, essentially fear, is persistent. And that fear usually leads to compliance. That makes the cop's job easier and less risky.
For the cop, the only rational choice is to kill the dog.