I find it interesting you guys think the preachy stuff is limited to one episode (the most blatant I'll give you). Roddenberry (I gather it was him, since he reportedly did a re-write on nearly every Season 1 episode) seemed to slip it in to many episodes in less than blatant ways. At every turn in Season 1 is some kind of underhanded crack at 20th century humans expense.
Nightdiamond's post explained it quite well, suddenly there would be an extended diatribe that no one asked for and wasn't really called for in the situation, etc.
The back and forth with Q about being savages, etc. from Encounter at Farpoint is a big one of course. Picard takes great offense at all this mostly silly posturing by Q. Picard's reaction seems like it should have been similar to Uhura's reaction to fake Lincoln's use of a dead term that was once controversial, which is to say, it shouldn't have bothered him much, and he should have mostly just found it ignorant and moved on (not unlike Kirk finding Trelane to be a bit silly and ignorant thanks to his forgetting to compensate for the time light travels), but of course then we wouldn't of had half of the pilot episode plot.
Go back and look at how episodes in Season 1 call many of the societies the crew encounter to be like "20th century Earth", others are just implied, and then basically there are lessons to be taught to these people by the great 24th century crew.
Ligonians from Code of Honor
Frengi's are old Earth "Yankee Traders"
The society on Angel One is literally said to be like 20th century Earth aside from dominant gender role flip/flip.
The whole thinly veiled '80s cocaine plotline in Symbiosis
The preaching exposition seems terribly ethnocentric (Federation-centric), for lack of a better term, and really kind of counter to the Starfleet mission, that kind of exposition is really an odd thing to put in to the mouths of people who were supposed to have moved on from being petty.