The underlying psychological issue about what age to bring puppies home involves socialisation. You can think of socialisation as a process where the dog learns how to deal with the living things in its environment—specifically dogs and people. The scientific foundation for our knowledge of socialisation in dogs begins with the classic book by John Paul Scott and John Fuller which was published in 1965*. It summarized 13 years worth of research which was done at the Jackson Laboratories in Bar Harbor, Main.
According to that research the ‘socialisation period’ starts at three weeks and extends to week 14. It is during this period that puppies learn to be dogs. As they play with their littermates they mimic fighting, hunting, catching and guarding behaviours. It is in this way that the pups develop the skills they will need later in life. They learn the behaviours associated with dominance and submission, and also basic communication skills at the same time. If they are bred in an environment where they have frequent interactions with humans, they also learn to associate with and bond with people.
The suggestion is that socialisation of dogs with other dogs comes first (from 3 to 6 weeks), and socialisation of the dogs with people comes next (from 6 to 14 weeks). If puppies do not have a chance to start socialisation during these time periods then the chance that the dogs will ever be properly socialised becomes very small indeed. A poorly socialised dog is apt to be more fearful and will have difficulty fitting in to the world of dogs or people, which means that it is not likely to succeed as either a pet or a working dog.
Furthermore the effects were much greater in dogs purchased from pet stores who most likely had less opportunity to interact with people and other dogs on a regular basis. It is clear that early separation from the litter is bad for puppies and results for a higher incidence of problems when the dogs are adults, in all probability because it interrupts their behavioural development by taking away needed social interactions before they are fully socialised.