A radiative model of quark and lepton masses utilizing the binary tetrahedral (T′) flavor symmetry, or horizontal symmetry, is proposed which produces the first two generation of quark masses through their interactions with vector-like quarks that carry charges under an additional U(1). By softly-breaking the T′ to a residual Z4 through the vector-like quark masses, a CKM mixing angle close to the Cabibbo angle is produced. In order to generate the cobimaximal neutrino oscillation pattern (θ13≠0,θ23=π/4,δCP=±π/2) and protect the horizontal symmetry from arbitrary corrections in the lepton sector, there are automatically two stabilizing symmetries in the dark sector. Several benchmark cases where the correct relic density is achieved in a multi-component DM scenario, as well as the potential collider signatures of the vector-like quarks are discussed.