It comes from Starfleet, to be sure. Only THEY know why.
Do we have any other proof of that, except that one Picard line?
Apart from the general lack of willingness by officers to refer to themselves as a military,
False. There has only ever been one time in canonical
Star Trek in which an officer of the Federation Starfleet (FSF) refused to refer to the FSF as a military, and that was Picard in "Peak Performance."
KIRK: I agree there was a time when war was necessary, and you were our greatest warrior. I studied your victory at Axanar when I was a cadet. In fact it's still required reading at the Academy.
GARTH: As well it should be.
KIRK: Very well. But my first visit to Axanar was as a new fledged cadet on a peace mission.
GARTH: Peace mission! Politicians and weaklings!
KIRK: They were humanitarians and statesmen, and they had a dream. A dream that became a reality and spread throughout the stars, a dream that made Mister Spock and me brothers.
Though outdated by subsequent episodes, the general implication here is that Starfleet is either attempting or has already managed to reduce its military role to a secondary aspect.
You are confusing the legal status of
being a military with the act of undertaking a war.
Clearly, the FSF is an organization that tries to avoid conflict whenever possible and encompasses duties beyond defense. This does not mean it it is not a military. The United States Coast Guard encompasses plenty of duties beyond war, yet it is still a military organization. The Canadian Forces views the delivery of humanitarian aide to be amongst its primary objectives, yet it is still a military.
Don't conflict a legal classification with an organization's
ethos. You can have a military that is not militarist
ic -- one which does not in general favor violence even as it remains the state's official defense agency.
If you try to make this consistent with ENT,
There is no reason to do this. The United Earth Starfleet (UESF) is no more the same organization as the Federation Starfleet just because they both have the word "starfleet" in their name than the
Massachusetts State Navy is the same organization as the United States Navy just because they both have the word "navy" in their name. As such, there's no reason to bring the legal classification of the UESF into consideration. It is utterly irrelevant to the legal classification of the FSF.
The point is the only time Starfleet officers make ANY self-description vis a vis their status as a military, it's always in the negative, or as an ambiguity.
This is not true.
Kirk refers to himself as a soldier in "Errand of Mercy," as did Nog in "
Valiant." Starfleet is explicitly described as operating a system of courts-
martial in numerous episodes, most especially "Court-Martial." Starfleet is described as a military on numerous occasions in "Homefront"/"Paradise Lost." Pike urges Kirk to
enlist in Starfleet in ST09 without it ever being seen as a bad thing. When David objects to the idea of Starfleet, the "military," controlling the Genesis research, Carol replies that Starfleet has kept the peace for a hundred years and does not object to the idea of their being a military.
Really, the only reference to the Federation Starfleet not being a military is from "Peak Performance." The preponderance of evidence is that Starfleet is a military and that no one has a problem with this -- but that Starfleet does not have a jingoistic ethos, unlike many present-day militaries.
Speaking from a "real world" rather than "in universe" perspective...
Starfleet was obviously originally created as a military organization. Roddenberry originally referred to it as "Captain Horatio Hornblower in outer space." Kirk said he was a soldier, not a diplomat. And, as Harve Bennett once observed, it was Roddenberry who put phasers aboard the Enterprise.
Later, as Roddenberry was elevated to quasi-deity status by the fans and began to pursue this notion that he was a great visionary, attempting to argue that Starfleet was not a military was one of the many changes in attitude he had. That was carried over into the on-screen attitudes of characters like Picard.
Simple as that.
On the other hand we have this:
Whom Gods Destroy said:
GARTH: Upon the firmest of foundations, Mister Spock. Enlightened self interest. You, Captain, are second only to me as the finest military commander in the galaxy.
KIRK: That's very flattering. I am primarily an explorer now, Captain Garth.
Metamorphosis said:
MCCOY: Maybe you're a soldier so often that you forget you're also trained to be a diplomat. Why not try a carrot instead of a stick
I think GR always wanted Starfleet (and Kirk) to be a multipurpose/mission organization.
Historically, real militaries have conducted diplomatic and scientific/exploratory functions. This does not mean they are not militiaries -- being a military, after all, is a legal status characterized by the organization in question being raised by the state to serve as its official defense organization in times of conflict. Having other duties in addition to that does not mean that the military ceases to be a military, too.