Or then the exact opposite - if there's no data on it, it may either be a marginal phenomenon or then not exist at all.
"Fleet captain" obviously exists as a thing. It's mentioned right there in the dialogue. You're building speculative castles in the air out of the fact that it wasn't mentioned anywhere
else in Star Trek.
Why insist the dialogue refers to one and the same event or timeframe? Why isn't that conflating of ceremonies, when two functionally distinct ceremonial occasions are indeed being mentioned?
There is
no mention of ceremonies, for either Pike being promoted or Kirk taking command of the
Enterprise. Kirk only talks about a
timeframe. It is, implicitly and logically, the
same timeframe for both events.
Absolutely not. There is no "when" there in the dialogue, and inserting a "when" there would alter the whole gist of it.
Once again, the dialogue in question:
MENDEZ: You ever met Chris Pike?
KIRK: When he was promoted to Fleet Captain.
MENDEZ: About your age. Big, handsome man, vital, active.
KIRK: I took over the Enterprise from him.
Kirk literally uses the word "when." Whatever difference you think that would make, was made.
Yes, but since we are discussing the intricacies of captaincy, which is both a title and a rank, I feel we should tackle rank...
Insisting that only people wearing the |:| braid can be captains is fallacy, as seen all across TOS, and never mind the spinoffs. Once we accept that, the Pike timeline becomes more malleable
Speaking for myself, I'm not insisting anything at all about sleeve braid. As I've already mentioned, I really don't care about sleeve braid (or, in the TNG era, about rank pips); I'm more than happy to disregard them in favor of pretty much
any other evidence from actual story or dialogue. There's simply nothing in Trek to suggest that either Pike or Kirk was anything other than a captain by rank when we saw them serving in the role of captain, and lots and lots of evidence (plus dicta from creators' intent) to indicate that they were. To say otherwise is, again, an exercise in sheer speculation.
...no reason to believe in the complicated. Going back to the original material makes things much easier: nobody mentions graduation in this context, only the act of "leaving" the Academy.
I don't think you're using the word "complicated" here in the way most people would understand it.

When people talk about when they left school, they're almost invariably talking about when they graduated, and vice-versa. That's certainly the way Kirk's dialogue in "Obsession" was intended to be understood. Other speculative interpretations aren't completely foreclosed, I suppose, but they're certainly not
necessary... because they're more complicated.
And we know Kirk was instructor at Lieutenant rank. So all his early occasions of holding commissioned rank can and should be interpreted as him having graduated.
Undeniably, that line from Mitchell in "WNM" has been tying people in knots for years. One could chalk it up to "early episode weirdness," but even within the context of just that episode it's problematic, since the overall impression is that Kirk and Mitchell are peers and old friends from Academy days, yet that line implies that Kirk was already an officer and an instructor there while Mitchell was still an underclassman.
Different fans and Trek authors have attempted to square this circle in a wide variety of ways, because there's really no simple solution. Personally, I'm partial to the hypothesis (as discussed in other threads around here) that Lt. Kirk took a year's leave from space duty after the trauma of the
Farragut incident, and spent it at the Academy, teaching and (perhaps) going through an extra year of grad-level "command school" himself. In this scenario, Mitchell would've been joking about what he'd heard second-hand from students at that time, but wouldn't actually have been a student of Kirk's himself. Yes, it's completely speculative, but it seems reasonable to me.
That complicated bit aside, though, fortunately the rest of Kirk's pre-
Enterprise backstory hangs together in fairly straightforward fashion. We know that he and Mitchell had known each other for 15 years before "WNM"; that he was a plebe (i.e., freshman) 15 years before "Shore Leave" (season 1), at which time he dated Ruth and was hazed by Finnegan; that he was a "new fledged cadet" when he participated in the Axanar Peace Mission ("Whom Gods Destroy"), for which he received a decoration ("Court Martial"); that he was an Ensign aboard the
Republic when he reported the error of his erstwhile instructor Finney ("Court Martial"); that upon leaving the Academy his first commander was Captain Garrovick of the
Farragut ("Obsession"); that that his first planetary survey mission, when he was a Lieutenant, was to Neural, 13 years before "Private Little War" (s2); and that Garrovick died when the
Farragut was attacked 11 years before "Obsession" (s2), while Kirk was still a Lieutenant. We can assume he rose to higher positions and presumably served as an XO on some ship(s) prior to
Enterprise, but it's never been specified in canon, although we do know that he dated Janet Wallace six years, four months before "Deadly Years" (s2) and Areel Shaw four years, seven months before "Court Martial" (S1). All that's from dialogue. Not a lot of complications there.
Should we for some reason assume Kirk and Pike are relative strangers to each other? That is, less intimate than, say, Kirk and Decker, or Kirk and Wesley?
Well, yes. If they were closer it seems more than likely that Kirk would've heard the news of Pike's accident in the months since it happened, but in the opening of "The Menagerie" we learn he hadn't. Spock had, but we know he
was close to Pike.
It seems Spock feels the need to shield Kirk from the "subspace buzz" on Pike's fate - an action unnecessary for his plan of abducting Pike. Had Kirk known about Pike, he might well have paid a visit to SB11...
Or, I suppose, one could find a way to conclude the exact opposite. You seem to be using Occam's Razor in an interestingly inverted fashion in this thread!...
