The polarized strange quark puzzle concerns the fact that the polarized strange quark density extracted from polarized inclusive deep inelastic scattering data is significantly negative, whereas it is zero or slightly positive when extracted from a combined analysis of polarized semi-inclusive and inclusive deep inelastic data. SU (3) flavor symmetry, which, it is generally accepted, is not an exact symmetry, plays an important role in the inclusive analysis, and all the extracted polarized quark densities depend, to some extent, on the level of symmetry breaking introduced. But by far the most sensitive to the breaking is the strange quark density. In this paper we present a NLO QCD analysis of the world data on polarized inclusive DIS data on protons, neutrons and deuterons, including the final JLAB CLAS/EG1b data on the proton and deuteron, and study the sensitivity of the strange quark polarization to the breaking of flavor SU (3).