It seems that the quark pair superconductor can be odd or even parity pairing respect to the parity $P$.
Say that the even parity has the form: $$ \langle\psi C \gamma^5 \psi\rangle $$
the odd parity has the form: $$ \langle\psi C \psi\rangle $$ There is no difference at perturbative computation. $C$ is charge conjugate matrix.
But the literature seems to suggest that instanton effect favors the even parity not the odd parity. I look into the literature but the original paper seems not to assert that claim. Refs cited here
Do you have either a simple and intuitive or a rigorous analytic explanation of the claim?