As I understand it (and please correct me if I'm wrong if anyone has more accurate information),
The dogs were off leash and effectively out of control.
They attacked another (leashed) dog which panicked and tried to escape wrapping the owners legs with the lead. The woman screamed and fell (some reports say into the road - others don't mention this). Her dog was injured.
The dogs continued to worry at the woman's smaller dog. A passer by who saw what was happening understandably thought he woman was being attacked and called the police.
Someone apparently told the owner to put his dogs on a lead - he refused, got hold of their collars and started to leave with them.
The police arrived (presumably with a marksman - I think that this was precautionary as there have been some horrific dog attacks lately, and they had no idea what they might be facing).
The owner saw the police and at that point leashed his dogs, but continued to leave the scene. The police followed and asked him to stop. He refused. They told him the needed to see the dogs and check them for injuries. He refused to stop and continued on his way. An argument ensued. The dogs - already high on adrenaline following the attack on the woman's dogs - were barking and behaved in a way that suggested that they had become over-excited (and bear in mind that when any dog is over-excited, accidents can easily happen).
Owner refused to hand the dogs over (I imagine because he was banned form keeping dogs after his previous three dogs had attacked and killed another one). The police warned him, very clearly "If you don't hand them over we'll have to shoot them".
He replied "Shoot them then." and released the lead of one of the dogs which ran towards the police officers. It didn't have a lot of ground to cover - the two groups (man and dogs/police) were quite close. The marksman shot it.
I saw the shooting of the first dog, which looked to me like an accurate, clean kill, in the video.
I didn't see the shooting the second dog which was apparently cowering with fright and was also apparently caught by one of those poles.
It later transpired that the woman had not been bitten but her dog had (however if it is correct that she fell into the road she could easily have been hit by a car).
I love dogs. I have never had less than three, and at one time had eight in the house - my own 6 and my daughter's 2, and I found this was a very distressing, but I honestly don't think that the police could have acted any other way under the circumstances.
The dog running towards the police officers could easily have bitten someone if it felt its owner was under threat; the other dog may have "cowered" but that doesn't mean it wasn't dangerous- frightened animals often are.
The one and only person responsible for this awful incident was the owner.