An analysis of the forward-backward asymmetry (FBA) in the decay B-+/- -> (KKK +/-)-K-+/--K--/+ is carried out based on the LHCb data. It is found that the large FBA observed for the invariant mass of the K+ K- pair around 1.5 GeV can be explained by the interference of the amplitudes between the resonances with even and odd spins, where the former can be the spin-0 f(0)(1500) resonance plus a nonresonance s wave, while the latter is a spin-1 resonance which is probably rho(0)(1450). This is in contradiction with the conclusion of former experimental analysis [e.g., BABAR, Phys. Rev. D 85, 112...