I can fully appreciate Assemblyman Lloyd Levine's concern about the fact that our animal shelters are over-run with unwanted dogs and cats. This is a serious humane issue that more people need to attend to.
However, allowing only purebred dogs in our society in the years to come is definitely not the solution. Purebreds are prone to many health problems due to a limited and closed gene pool. Without an introduction of new and unrelated genes, creatures lose genetic diversity, which leads to weaker animals.
I am a responsible pet owner of mixed-breed, spayed and neutered dogs and cats, and have always been. My dogs and cats have lived long, happy lives with few health problems. I wouldn't exchange them for the world.