superconductivity - Quark pair superconductor: Even parity is favorred than odd parity

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?