The two electrons settled in the same orbit of an atom have one up and one down spin - so the net spin, and hence the magnetism becomes zero. If, at the end, one unpaired electron remains, the atom has a net spin and is magnetic.
As a large solid, the atoms form a crystal structure and interact with each other through these valence electrons. The valence electrons are not localized to an atom in a crystal lattice. They are randomly distributed in the whole crystal lattice. Thus the solid becomes non magnetic due to this random orientation of the valence electrons.
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