Pion decay to two photons is electromagnetic (the original flavor chiral anomaly). But decay to two neutrinos could only go through a box diagram involving two Ws of opposite charge: the quarks or antiquarks hairpin of the pion wavefunction has to decay to a virtual $W^+ ~ W^-$ pair, which then connect to a similar hairpin involving a virtual charged lepton and a $\nu ~\bar \nu$ pair of decay product particles.
- That, then, entails a doubly weak suppression, by, at the very least, a factor of $(m_\pi/M_W)^8$ ... twenty two orders of magnitude. Hopeless.
As for parity, indeed, the doubly weak interaction blasts parity to vapor, but further consider that a neutrino-anti neutrino pair has the parity of a quark-antiquark pair…