I agree that irresponsible dog owners who do not sufficiently control their animals are to blame for most of the problems and the horrendous attacks that have taken place. But, without taking away from the need to address this terrible problem, I would also suggest that some parents also need to control their children better.
I have a six month old collie cross. He is extremely friendly and loves everyone, to the point where he wags his tail and his whole body at everyone we meet. He is endearing, and naturally children are drawn to him. Having only just begun puppy training classes, he is still quite boisterous when he gets attention, so I keep him on a lead at all times, and a very short lead when he is meeting children. The other day at the beach, one small child (about 4 years old, with her mother) was really taken with him - she petted him for a long time, while I held his collar. He loved it and so did she. We walked on, the child ran after us. I stopped again, I held his collar and allowed her to pet him again. This happened four times, while the mother made no attempt to stop the child running after us. Eventually I asked the mother if she could prevent the child running after us as we needed to walk on and the dog was becoming over-excited. We walked away, I released the dog's collar (he was still on his lead), the child suddenly reappeared, took me by surprise, the dog, already excited, was overjoyed, leapt at the child, and knocked her down. Thankfully, she was unhurt, but she was shocked, and cried. The dog thought it was great fun. The mother was furious because the dog had knocked down the child. I was furious because the mother did not control the child. Had this gone to a complaint, the dog would have got the blame. It was not the dog's fault, nor the child's fault. It was the mother's fault. But I would have been penalised and my dog may have been perceived to have "attacked" this child. I do not want this story to seem to minimise the seriousness of attacks by dogs, especially the horrendous attack by a pack in a park, during which two dogs were shot dead. But some parents need to learn common sense when their children are around dogs.