Private shelters are the ones that don't euthanize. Most county shelters are supported by tax dollars are are only required to keep an animal for a short period of time before euthanizing them. Sadly, there are just too many unwanted cats and dogs and they must keep making space for more.
The only way to stop this horrible cycle is to spay and neuter our pets.
Did you know that 25% of all the dogs in shelters are purebreds? And that it's the backyard breeders, not the puppymills that are responsible for most of the purebred dogs who end up in shelters.
Please read this:
ShelterDog Rescue - Are you a BackYard Breeder?