Any number of animal activists say that no more animals should be bred until the shelters are empty and the shelters no longer kill any animals.
I bought this bridge from a crazy-eyed man for $50 and my soul, but the tolls that I collect at both ends of the bridge will make me rich, rich rich.
What's wrong with their logic? What's wrong is that if there is any substantial number of dogs in any city, some are going to die in shelters. Trying to reduce the number of shelter deaths by reducing the number of animals out there might work, but we will never reach zero. These people have announced that they will fight a war against our ownership rights forever. They know that shelter deaths will never reach zero. If we accept their conditions they have trapped us into an agreement to do the impossible. We will have handed over our rights in order to satisfy their delusion.
If nothing else the AR people will breed dogs themselves and kill them in their own shelters. This is actually a practice that dates back to the 19th century and ASPCA people were caught doing it.