kittel: possible states of magnetic

I do not understand the attached picture excerpt from Kittel Thermal Physics (first sentence up to 'eqn' (7) ).

I would expect the moments to go down in increments of one, not two. I think the subsequent paragraph tries to explain why, although I am not sure this is indeed the purpose. Could anyone please shed some light on this horribly explained section?

Thanks!

Attached Images

kittel_15.jpg (108.8 KB)