  We calculate the next-to-next-to-leading-order (NNLO) perturbative
corrections to $P$-wave quarkonia annihilation decay to two photons, in the
framework of nonrelativistic QCD (NRQCD) factorization. The order-$\alpha_s^2$
short-distance coefficients associated with each helicity amplitude are
presented in a semi-analytic form, including the "light-by-light"
contributions. With substantial NNLO corrections, we find disquieting
discrepancy when confronting our state-of-the-art predictions with the latest
\textsf{BESIII} measurements, especially fail to account for the measured
$\chi_{c2}\to\gamma\gamma$ width. Incorporating the effects of spin-dependent
forces would even exacerbate the situation, since it lifts the degeneracy
between the nonperturbative NRQCD matrix elements of $\chi_{c0}$ and
$\chi_{c2}$ toward the wrong direction. We also present the order-$\alpha_s^2$
predictions to $\chi_{b0,2}\to\gamma\gamma$, which await the future
experimental test.
