Refuting a cause (ce n'est pas que)

To be polite when declining an invitation, you often need to clarify that the rejection isn't personal.

"Not that": Non que

Use non que (not that) to explicitly reject a possible reason or assumption. Because the rejected reason is false, it requires the subjunctive mood.

I am unavailable tonight, not that I want to avoid this commitment.
Je suis indisponible ce soir, non que je veuille éviter cet engagement.

"It is not that": Ce n'est pas que

Ce n'est pas que (it is not that) is slightly more conversational and also triggers the subjunctive. It is often followed by mais (but) and the indicative mood to state the actual reason.

It is not that I want to cancel, but I am overloaded.
Ce n'est pas que je veuille décommander, mais je suis surchargé.

Use the noun un empêchement to express a last-minute, unavoidable scheduling conflict.

I have a scheduling conflict, not that I am tired.
J'ai un empêchement, non que je sois fatigué.

If you have a conflict, you might need to push back (décaler) the commitment rather than canceling it altogether.

It is not that I am forgetting this commitment, but we must push it back.
Ce n'est pas que j'oublie cet engagement, mais nous devons le décaler.

Using these structures allows you to gracefully decline an offer (décliner l'offre) while firmly stating your boundaries.

It is not that he is lazy, but he is overloaded and must cancel.
Ce n'est pas qu'il soit paresseux, mais il est surchargé et doit décommander.