1. Breed only when you want another dog to show.
2. Never breed a dog with a health problem.
3. Breed only the best to the best.
These statements probably originated among breeders of approximately the top ten breeds (in terms of breed popularity) of purebred dogs. After all, those breeders produce approximately 50 percent of all purebred dogs. Many of these breeds have an overpopulation problem, as is evidenced by the number of dogs of those breeds that show up in rescue. And these breeds have large gene pools.
However for the numerically smaller breeds - such as my breed (Norwich terriers) - I think these statements are poor advice. Breeds with small closed gene pools need to do everything that they can to increase their gene pool. They need genetic diversity ... otherwise the breed will die out. In an ideal world, every female would be bred and every male would be bred. This does not happen, as breeders apply selection pressure and only breed some of their dogs. This restricts the gene pool. Only breeding when one wants another dog to show restricts the gene pool even more.
Obviously one should not breed unless one is confident that all the puppies will end up in good homes (which might be the home of the breeder). In my breed (Norwich terriers) there is a high demand for puppies and a small supply. So good homes are not a problem.
Regarding health, there is no perfectly healthy dog. Every dog has some health issues or carries genetic mutations that will cause health problems in the dog's progeny. Most dogs - like most people - are generally healthy. But "perfectly healthy" does not exist - either in dogs or in people. (And to anyone who thinks they have a perfectly healthy Norwich terrier, I will pay them $1,000 if their dog can pass or get perfect scores on several health tests that I will state.) So not breeding dogs with a health problem will wipe out dog breeds.
Of course, dogs with severe health problems should not be bred. Each breeder has to decide what they think is an appropriate level of severity. Each breeder has to decide what level of risk they are willing to accept regarding health issues when doing a breeding. (Sadly, too many breeders take the "head in the sand" approach with regard to health risk and do not health test.) Different breeders will have different levels of comfort on different health issues. This is the "art" of breeding.
Finally, regarding the statement "Breed only the best to the best" this is somewhat of a tautology. Of course a responsible breeder is going to try to improve his or her breeding stock. But "best" may mean what they have available to them ... both in terms of geography and availability. While shipping semen is possible, it is both more expensive and less successful in terms of a successful pregnancy than if the dogs are together. So often breeders are limited to dogs in their geographical region. And often a desirable dog is not available for breeding for any one of several reasons: the desirable dog's owner may not think it is a good match, the dog is traveling, etc. And while Hollywood may perpetuate the idea of a "one true love", the reality is that there are several good breeding candidates who are "good enough".
The goal of selective breeding is to improve. But this does not require drastic culling - as these three dog breeder statements seem to advise. I think these statements of advice can be safely ignored by breeders of numerically small breeds.