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

It follows the phrase ce n'est pas que (it is not that), which is used to reject or refute a reason. Because you are denying that this is the real cause—meaning it is not a reality—French requires the subjunctive.

Why is the indicative est used in the second half (mais il est surchargé) if the first half triggered the subjunctive?

While the first part denies a false reason, the second part (mais il est surchargé) states the actual, factual reason for his cancellation. Since it is a confirmed reality rather than a rejected one, it uses the indicative.

Is there a difference between décommander and the more common verb annuler?

Yes, though they are often interchangeable here. Annuler is a general word for "to cancel" (a flight, a project, a subscription). Décommander is more specific and usually means to cancel a scheduled appointment, a reservation, or an invitation with someone.

Does surchargé just mean "very busy"?

It is stronger than just being busy (occupé). Formed from sur- (over) and chargé (loaded), it literally means "overloaded." In this context, it implies he is completely overwhelmed with his schedule or workload.