Recently deep inelastic scattering experiments have implied that the ‘sea’ of the nucleon breaks flavor SU(2) symmetry. We examine the possible origins of this symmetry breaking in the Fermi statistics of the quarks and antiquarks in the sea and the requirements of chiral symmetry. We show that the present data have a natural explanation in terms of the long-range pion structure of the nucleon. Further work may lead to useful bounds on the parameters of bag models of the nucleon.