If a dog nips at you that is one thing. That can be trained out of it. If a dog bites someone, that can also be trained out of it, and I generally recommend working it out with the owners before reporting it to the law. However, if the owner cannot show responsibility and signs of immediate containment and future improvement in an appropriate time frame, and there are children involved, I believe it is time to give the owner notice that you will be in contact with authorities.
I'm all for giving the dog multiple chances, and generally against government involvement due to the inflexible nature in a situation that requires a tailored approach, but I'm not going to hold that with greater weight then the safety of children, and will allow only so much.
As put in my headline, it really depends on the circumstance. If a human clearly provokes a dog and angers it the dog has every right to be angry and potentially attack.
Also if the dog is playing or thinks he/she is playing and bites in a playful manner which unintentionally seems vicious that isn't fair either.
Dogs don't know the difference between right or wrong. If they knew biting someone viciously, intentionally or unintentionally, would cost them their life I'm sure they'd avoid doing so. But they don't know whether they are doing right or wrong. Also if an owner brings up the dog badly it isn't the dog's fault at all.
I think dogs should not be executed for biting someone people are not killed for killing another human or animal. Its not fair and plus their a lot less dogs then there are humans. If a dog bites someone they shouldn't be killed, instead they should go through some pet training to help them to stop biting people and other animals.