  We develop a class of left-right symmetric theories based on the gauge group
$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)$ with a generalized seesaw
mechanism for generating the charged fermion masses. Neutrinos are naturally
Dirac particles in this setup with their small masses arising from two-loop
quantum corrections. We evaluate these two-loop diagrams exactly and analyze
the flavor structure of the lepton sector. We find excellent fits to neutrino
oscillation data, independent of the right-handed gauge symmetry breaking
scale. We also explore the possibility that neutrinos are pseudo-Dirac
particles in this framework, with the tiny mass splittings between active and
sterile neutrinos arising from Planck-induced corrections and find possible
realizations. These models can be tested in the near future with precision
cosmological measurements of $\Delta N_{\rm eff}$ in CMB which is predicted to
be $\simeq 0.14$. This class of models allows for a solution to the strong CP
problem via parity symmetry without the need for an axion.
