  The Type I, II and hybrid (I+II) seesaw mechanism, which explain why
neutrinos are especially light, are consequences of the left-right symmetric
model (LRSM). They can be classified by the ranges of parameters of LRSM. We
show that a nearly cancellation in general Type-(I+II) seesaw is more natural
than other types of seesaw in the LRSM if we consider their stability against
radiative correction. In this scenario the small neutrino masses are due to the
structure cancellation, and the masses of the right handed neutrino can be of
order of O(10)TeV. The realistic model for non-zero neutrino masses, charged
lepton masses and lepton tribimaximal mixing can be implemented by embedding
$A_4$ flavor symmetry in the model with perturbations to the textures.
