Because I'd more than happy to get the nails to hammer into that particular coffin.
I never believed that Benedict Cumberbatch was playing Khan. Abrams and Co. said that they were remaking any of the TOS movies and putting Khan in the second one would have gone counter to that statement. Following that line of thought, there would be no emotional investment if they went "Hey here's Khan Noonien Singh and he's plotting revenge against Captain Kirk!" because without "Space Seed", Khan is just a guy who doesn't like Kirk and then the movie falls flat on its face.
I think John Harrison (if that is indeed the character's real name and not a red herring) is a member of Section 31. In the trailer, he's described as one of Starfleet's top agents and that ultra-clandestine organization called Section 31 is (nominally) a part of Starfleet. It might also go to explain his uniform. We know, thanks to Star Trek: Enterprise, that the organization existed as far back as the 22nd century and we can presume that the events of Enterprise happened in the new continuity, since they preceded the point of divergence in the 2009 reboot. Then again, he could just be a member of Starfleet's Intelligence branch.
As for Harrison's motives, he mentions a crime committed by Kirk's "commanders" (presumably Starfleet brass) that he sees as 'unforgivable'. A previous trailer showed him volunteering his services to help the family of a dying girl, so maybe Starfleet was in the position to help her and others afflicted with the same condition, but didn't and now he's out for revenge. Or maybe he sees Starfleet (and by extension, the Federation) as corrupt and plots to overthrow one or both.
The possibilities certainly makes me anxious for May to get here so that I can find out.