Gyrokinetic theory and simulation find that the nonlinear self-interactions of the long wavelength geodesic acoustic mode (GAM) in toroidal plasmas cannot efficiently generate the second harmonic due to a cancellation between the perpendicular convective nonlinearity and the parallel nonlinearity, which is neglected in most of gyrokinetic theory and simulation. Other mechanisms beyond conventional GAM theory are required to explain recent experimental observations of the excitation of the GAM second harmonic.