Why did Old French borrow de- to mean "academic degree", not sup-?

Question

I hope my befuddlement is self explanatory and obvious. In Modern English and French, degrade and degrader still negatively connote debasing or demeaning. But academic degrees, goals, and progress are associated with "up" and "above", not "down" or "de-". Why did Old French prefix de- to gradus, not sup-?

degree | Search Online Etymology Dictionary

c. 1200, "a step, a stair," also "a position in a hierarchy," and "a stage of progress, a single movement toward an end," from Old French degré (12c.) "a step (of a stair), pace, degree (of relationship), academic degree; rank, status, position," which is said to be from Vulgar Latin *degradus "a step," from Latin de- "down" (see de-) + gradus "a step; a step climbed;" figuratively "a step toward something, a degree of something rising by stages" (from PIE root *ghredh- "to walk, go").

degree [13]

Etymologically, degree means ‘step down’, a sense revealed more clearly in its relative degrade [14]. It comes via Old French degre from Vulgar Latin *dēgradus, a compound noun formed from the prefix dē- ‘down’ and gradus ‘step’ (source of English gradual and a wide range of other words). The word’s modern meanings, such as ‘academic rank’ and ‘unit of temperature’, come from an underlying abstract notion of a hierarchy of steps or ranks. Degrade represents a parallel but distinct formation, originally coined as ecclesiastical Latin dēgradāre and passed into English via Old French degrader.

Word Origins (2005 2e) by John Ayto, p 155 Right column.

Answer 1

The prefix de- had more than one meaning in Latin, and many of them persisted and developed over time. Like all core morphemes, the meaning is extremely hard to define and pin down the semantic nuances. At least we're only dealing with the bound morpheme here, not the free one, which has a 22,000-word definition! (Interesting how dictionaries went from defining rare words, which are easy, to common words, which are impossible...)

Here's the Wiktionnaire article on what de- could mean in Latin.

1. marque un mouvement de séparation, d’éloignement : decidere, etc.
2. renforce le sens du verbe, marque l’achèvement, la plénitude ou l’intensité : declamare, etc.
3. sens contraire, marque le manque ou la cessation : deformare, etc.
4. Il peut y avoir contraction : dego < de ago, etc.

Since our base morpheme is gradus "step, stage, rank, position" it would seem that degree is likely formed on the second definition, reinforcement, rather than on the first or third as Etymonline supposes. However, as hinted above, there are definitely more than just these four meanings of de- and perhaps another shade more closely aligns with their explanation. Either way, we are not limited to "the lack, cessation, reversal, undoing" sense.

Many other words are formed on similar senses of de-, including définir lit. "to set a finis, boundary"; délimiter in the same meaning; déclamer lit. "to cry out"; and so on. Look and you'll find that undoing is not the only sense.

We should observe that words can be derived multiple times throughout history from the same roots in different senses, ending up phonologically the same but semantically different. Hence "degrade" and "degree" have the same elements, but are not derived from each other; they were based on different senses of de-. Compare English be-, which can mean either "provisioned with" as in "befeathered", or "to remove" as in "beheaded". Either of those could easily have had the opposite meaning of the one they have.