Originally Posted by Captain Pike
Admiral? He makes Admiral? In the canon timeline in the Menagerie Mendez said he was Fleet Captain. Greenwood did say over at trekmovie that he is open to returning for the sequel. Maybe he will send Kirk on the five year mission or does he do it at the end in this movie?
I suspect Pike was made Admiral because there's a precedent in TREK films for Admirals = not bridge captains, which is what Kirk is being made. The term "Fleet Captain" (is this even common in our military??) might just be confusing, as if there would be two captains on the Enterprise.
When Kirk was made Admiral, he was taken off the bridge and got 'desk duty', which is what Pike is capable of (for now), so there's some established 'definition' of the Admiral promotion involved.
Basically, I think the switch in ranks simplifies matters for the audience as the film ends, right when they don't want to explain a lot of things to spoil the moment.