Despite some progress in understanding the family flavor mixing problem, one still has the uneasy feeling that, in many cases, the problem seems just to be transferred from one place to another. The peculiar quark-lepton mass hierarchy is replaced by a peculiar set of U ( 1 ) F flavor charges or a peculiar hierarchy of the horizontal Higgs field VEVs in the non-abelian symmetry case S U ( 2 ) F or S U ( 3 ) F . As a result, there are not so many distinctive and testable generic predictions relating the weak mixing angles to the quark-lepton masses that could distinctively differentiate the one family symmetry model from the other. This indeed related to the fact that Yukawa sector in the theory is somewhat arbitrary as compared with its gauge sector. Actually, one can always arrange the flavor charges of families or the VEVs of horizontal scalars in these models in a way to get the acceptable hierarchical mass matrices for quarks and relatively smooth ones for leptons.