The dwarven boarding school system is designed for the betterment of dwarven society as a whole and to place dwarves where they are most likely to succeed, with no regard for family values, pedigree, personal choice, individuality, or social status. Incompetent dwarves will not rise due to nepotism, and skilled dwarves will not be smothered by social conventions.
In short, the dwarves love Plato's Republic, or at least some of the hypothetical cities described therein.
Among other topics, Plato discusses how to properly raise children in several hypothetical 'just' societies, and describes systems that fit your scenario pretty well:
Now early life is very impressible, and children ought not
to learn what they will have to unlearn when they grow up; we must therefore
have a censorship of nursery tales, banishing some and keeping others.
The tale must be
imparted, first to the rulers, then to the soldiers, lastly to the people. We will inform them that their youth was a dream, and that during the time when they
seemed to be undergoing their education they were really being fashioned in
the earth, who sent them up when they were ready; and that they must protect
and cherish her whose children they are, and regard each other as brothers and
These brothers and sisters have different natures, and
some of them God framed to rule, whom he fashioned of gold; others he made
of silver, to be auxiliaries; others again to be husbandmen and craftsmen, and
these were formed by him of brass and iron. But as they are all sprung from
a common stock, a golden parent may have a silver son, or a silver parent a
golden son, and then there must be a change of rank; the son of the rich must
descend, and the child of the artisan rise
Since all dwarves are equal then all dwarven children are equal, and they must be removed from their families to receive an equal education in order to continue the dwarven meritocracy.
If children stay with their parents, then not all children will receive the same education: children of carpenters will learn carpentry, children of bankers will learn banking, etc. Furthermore, this may prevent them from rising to their true potential, as the child of a carpenter may never realize their natural skill at banking, or vice versa.