Comments on a Flavor Symmetry

It is pointed out that if a flavor symmetry (a discrete symmetry, a U(1) symmetry, and so on) exists, we cannot obtain the observed CKM quark mixing matrix V_q and MNS lepton mixing matrix U_\ell, even if we can obtain reasonable mass spectra under the symmetry. Such the serious constraint is derived only from the SU(2)_L conditions, and we will not assume any explicit flavor symmetry and/or any explicit mass matrix forms. And then, we will discuss the meaning of the severe constraint.