I staunchly oppose putting twins in separate classrooms when they prefer to be together.  As I explained before:

Sure, if you separate twins, they’ll make more friends.  But that
hardly means you’re doing them a favor.  The reason why twins put less
effort into making new friends is that they’ve already got a better
friend than most of us will ever have.  For twins, the marginal benefit
of trying to making new friends unusually small – and cliquishness is
their optimal response.

Now schools are discouraging best friendship altogether.  From Robin via the NYT:

The classic best-friend bond — the two special pals who share secrets
and exploits, who gravitate to each other on the playground and who
head out the door together every day after school — signals potential
trouble for school officials intent on discouraging anything that hints
of exclusivity, in part because of concerns about cliques and bullying.

Frankly and fortunately, I doubt the war on best friendship will get very far.  But this is indeed the slippery slope down which the main arguments for twin separation lead.