I realized all this several years ago. Spay/neuter programs are able to reduce the number of casual litters that used to result in much larger euthanasia figures, much of it by drowning or neck-wringing, but now that pets are an industry, euthanasia of pets is driven by the consumers' short interest span and the cheap price to buy and get rid of pets. Everyone who "handles" pets in anyway is part of the industry. Breeders, sellers, vets, trainers, food and accessories producers and sellers, "shelters", humane societies like the SPCA, pounds, and rescuers. We all make the product possible. We either produce, or sell, or own, or service, or dispose of pets, and without us there would be no pet abuse.
I realized to my dismay some time ago that by owning pets I am a link in the chain of animal use and abuse. I can only justify my part in this chain by only rehoming dogs that are suffering without any hope. Merely shuffling pets from one owner to another is to be well and truly part of the industry.
Animals should not be chained, either literally, or by the chains of dependence on us. And that is why I have said that one day I will not own one of the "slave species". I can't be part of what I hate and stay honest.