I had the same question until I realised it meant Google Cloud Messaging (or, this is how people seem to interpret it) - my initial thought was that it was about Galois Counter Mode (an authenticated encryption mode), and was curious why not using it was considered a benefit.

Threema does seem to use XSalsa20 + Poly1305 for authenticated encryption (not AES in GCM), btw.

a) I feel Google is over-represented in our tech lives, so when it's possible to use an alternative I choose to.

b) GCM undoubtedly collects metadata about my usage of it

c) [falsified] AFAIK GCM requires a Google account, which means your usage of the system is at the pleasure of Google, and can be disabled for a myriad of Orwellian reasons.