We reformulate the problem of a steerable left-handed antenna reported by Matsuzawa et al. [IEICE Trans. Electron. E89-C, 1337 (2006)] from the view point of structural electromagnetic resonance of the unit structure. We show that there are two such resonances with different spatial symmetries in the relevant frequency range, which result in the formation of two electromagnetic bands with opposite signs of curvature at the Γ point of the Brillouin zone. We derive an expression of dispersion curves based on the tight-binding picture and show that the dispersion of the two bands is linear in the vicinity of the Γ point in the case of accidental degeneracy only if the symmetry of the two resonance states satisfies certain conditions. We also show that the refraction angle can be designed by changing the lattice constant of the arrayed unit structures, since the band width is modified due to the change in the electromagnetic transfer integral.