Why do dictators in totalitarian societies enforce the living arrangement where children live apart from their families?

Of course, kids do not have to live apart from their
families in totalitarian societies.  The Nazis, for example, did not generally take kids
from their families.  Neither did the Communist Party in the USSR.  However, it makes
sense that dictatorial leaders such as the ones in this book would make kids live away
from their parents.

In Anthem, the
government does not want people to have individuality.  They have numbers rather than
names, for example.  They are also expected to treat everyone equally and not to have
special friends.  In this context, you can see why they would want to raise kids apart
from their parents.

If you grow up with your parents, you
form a family.  It is your "in group."  You identify most with your family and other
people are not as important to you.  When you do this, you form the idea that you are
different from everyone else.  In this book, the leaders want everyone to be the same so
that they will not try to rebel against the society.  The leaders want everyone to think
the same so that there will be complete social
stability.

This is why they raise kids away from parents. 
They want the kids to feel like they are just pieces in the large society -- not
individuals who are tied to certain families and friends.