With reference to the piece in Southwest Airlines' Spirit magazine that named Language Log one of "8 Diversions" for its readers, Chris Cieri pointed out to me that several phrases might in principle be either praise or criticism. For example,
These profs know their allomorphs from their morphemes, but their posts are anything but pedagogic.
Being someone with a positive attitude towards school, Chris observes that this might mean "These people know their stuff, but they can't explain it properly in what they write."
Unlike Chris, however, most English-speaking people over the past few centuries have had generally negative attitudes towards pedagogues and pedagogy, at least when they use words derived from Latin paedăgōgus, meaning "a slave who took the children to school and had the charge of them at home, a governor, preceptor, pedagogue". The OED's earliest citation for pedagogic is
1693 J. BARNES in B. Hawkshaw Poems upon Several Occasions p. v, Forward Sense, to lofty Flights enclin'd, Prevents the tedious Discipline of Schools, The Loyt'ring Art of Pædagogick Rules.
There's a slightly earlier one for the variant form pedagogical -- in Act I, Scene 1 of Mr. Anthony (a 17th-century play by Roger Boyle, Earl of Orrery, who died in 1679), Anthony expresses some hostility to his schoolmaster, Mr. Pedagog, in terms that are by no means respectful of the characteristic tools and methods of pedagogy:
Prethee let me have my full swinge at him (for he has had his many a dismal time at me:) I say, if thou dost not conform to all the Maxims of Jack Plot, Tom Art, and my own dear self, I will peach thee at such a rate to my Sire, as shall provoke him to uncase thee out of thy Pedagogical Cassock, Condemn to the Flame, Martyrlike all thy Ferula's, Grammars, Dictionaries, Classick Authors, and Common-Place Books; nay, take thy Green Glasses out of thy Spectacles, and leave thee only thy Horn-cases to look through; by which, thou wilt be as able to read Prayers with thy Nose as with thy Eyes.
Although the pedagogical cassock is now worn only for graduation rituals, the negative associations with teachers have remained in force over the centuries. Thus Caroline Kirkland, "The Schoolmaster's Progress", 1845:
Master William Horner came to our village to keep school when he was about eighteen years old: tall, lank, straight-sided, and straight-haired, with a mouth of the most puckered and solemn kind. His figure and movements were those of a puppet cut out of shingle and jerked by a string; and his address corresponded very well with his appearance. Never did that prim mouth give way before a laugh. A faint and misty smile was the widest departure from its propriety, and this unaccustomed disturbance made wrinkles in the flat skinny cheeks like those in the surface of a lake, after the intrusion of a stone. Master Horner knew well what belonged to the pedagogical character, and that facial solemnity stood high on the list of indispensable qualifications.
And a whole dissertation could be written about attitudes towards teachers in recent popular music, starting with
No more pencils
No more books
No more teachers' dirty looks
The AHD entry for pedagogic elevates this connotation to the level of a second sense:
1. Of, relating to, or characteristic of pedagogy. 2. Characterized by pedantic formality.
It's true that the turn of phrase "anything but X" can be either positive or negative, depending on the properties of X as evaluated in the context. But I think that "anything but pedagogic" is likely to be meant as a compliment -- and a bit of web search confirms this impression:
From James Hilton's "Was It Murder?" (emphasis added):
The study presented another striking change; under the régime of the Reverend Dr. Jury, who had been Head of Oakington in Revell's time, it had been a gloomy, littered apartment, full of dusty folios and sagging bookshelves. Now, however, it looked more like the board-room of a long-established limited company. A thick pile carpet, a large mahogany pedestal-desk, nests of bookshelves in the two alcoves by the side of the fire-place, a very few good etchings on the walls, and several huge arm-chairs drawn up in front of an open fire, gave an impression that was anything but pedagogic. And Dr. Roseveare himself confirmed the impression. He was tall (well over six feet), upright, and of commanding physique. Bushy, silver-grey hair surmounted a strong, smooth-complexioned face into which, however, as he gave Revell a firm hand-grip, there came a smile both cordial and charming.
Katie Savchuk, "Tom Robbins find life in the magically mundane":
Posted by Mark Liberman at June 8, 2007 09:54 AMRobbins forces you to ponder the philosophical conundrums of the universe, from the meaning of time to the value of civilization in an unadulterated flow of thoughts that is anything but pedagogical.
"The only truly magical and poetic exchanges that occur in this life occur between two people. Sometimes it doesn't get that far. Often, the true glory of existence is confined to individual consciousness. That's okay. Let us live in the beauty of our own reality," Robbins writes.
As clever as it is profound, Even Cowgirls Get the Blues is overflowing with expressions just outrageous enough to describe reality.