This is a great question and there are two main reasons
why we wait until 8 weeks of age:

#1) Young pups are physically mature enough to leave their mom as
young as 5 or 6 weeks of age. They have developed their strong
teeth that are capable of chewing food. They are not relying 100% on
mom anymore. But, it is not the physical maturity that is growing the
most these few weeks as much as the emotional side of your pup.
Within the confines of the whelping box the  young pups are learning
huge lessons from each other. At about 5 weeks of age they begin to
play quite roughly with one another. One pup will grab another pup's
ear and bite down hard in order to use it as a tug toy. Since, this hurts
the pup badly, it reacts by counteracting with a vicious bite back in
order to save it's own ear! The first pup immediately lets go of the ear
because now he hurts too! Although at first glance this may seem
just like simple puppy play - you need to understand what is really
taking place. When the first pup bites the other, and the other one
bites back the first pup - He learns quickly that if I bite - I am going to
get hurt as well. In a few weeks the pups learn this lesson very
concretely. If in contrast, they leave at 6 or 7 weeks of age, they may
not have yet had the opportunity to thoroughly learn their lesson.
Which means that you take home your cute new pup - he gets so
lonely and quickly decides to play with you since his littermates are
no longer anywhere to be found! He will grab your hand, or leg, or
ear, or whatever is within reach and chomp down with all of his
might! You may scream, put the puppy down or just tell him to cut
that out! But you do not have those sharp razor like teeth that his
brother has that are so fantastic at getting back at him! His littermates
are much more equipped for teaching this lesson than any human
can ever be! If left to learn like they should, you will have a much
more enjoyable time when you do finally get to bring him home.

#2) It is also a NYS law according to the Department of Agriculture
that breeders may not sell any dog or cat before the age of 8 weeks.