Do you believe you aren’t adding to the pet overpopulation problem if you find good homes for all your pet’s puppies or kittens? Then consider this:
Suppose there are 10 families in your community who want puppies and can provide good homes for them, but there are 15 puppies who need good homes. When each of the 10 families takes a puppy, there will be 5 “leftover” puppies who have no future except humane euthanasia. Then suppose you let your dog have a litter of five puppies. There are now 20 puppies in the community who need good homes… but still only 10 good homes available.
Even if you manage to place every one of your five puppies with one of the available 10 homes, there are now 10 leftover puppies where before there were only 5. You’ve created more animals, but you haven’t created more homes — just taken some homes away from other puppies and kittens, dogs and cats.
By allowing your pet to breed, you’ve increased the number of puppies who will have to be euthanized because no one wants them.