Can you fly over a Medium enemy creature in a 10ft tall corridor?

Question

Let’s say you, a Medium character, are in a 5ft wide, 10ft tall corridor, and that a Medium enemy creature stands in your way. You wish to go behind the enemy creature using your fly speed (either disengaging, or just not particularly caring about getting an opportunity attack).

Considering that you cannot go through an enemy creature’s controlled space (unless said creature is two size categories above you), but that Medium creatures control a space of 5ft on a side, can a Medium creature fly over an enemy Medium creature in a 10ft high corridor ?

The reason I’m asking is because in a game I played (where I was the flying character), the DM claimed that creatures control a bigger space vertically (10ft instead of 5ft, or 2 squares instead of 1), and therefore flying over the enemy in this case is impossible. I don’t recall any place in the PHB/DMG/XGR where vertical controlled space is to be bigger than what the size category says, but the DM seemed convinced he was correct. Maybe I’m missing something ?

Relevant rules :

you can move through a hostile creature's space only if the creature is at least two sizes larger or smaller than you

Each creature takes up a different amount of space. The Size Categories table show s how much space a creature o f a particular size controls in combat.

Medium 5 by 5 ft

A creature's space is the area in feet that it effectively controls in combat, not an expression of its physical dimensions. A typical Medium creature isn't 5 feet wide, for example, but it does control a space that wide.

Answer 1

It May Depend on the Creature (and the DM)

The rules are unclear on how high a "creature's space" is, and a DM may have to make a ruling. Unfortunately, "a creature's space" is defined only in a 2-Dimensional sense: on PHB, p. 191, it is defined entirely in terms of squares (not cubes).

Tiny: 2.5 by 2.5 ft

Small 5 by 5 ft

Medium 5 by 5 ft (etc.)

A DM will have to decide how tall a creature's "space" is when it comes up. This may be based not only on a creature's height (which might vary from about 4 feet for dwarves to about 8 feet for hobgoblins), but also by the space they control. As you stated:

A creature's space is the area in feet that it effectively controls in combat, not an expression of its physical dimensions. A typical Medium creature isn't 5 feet wide, for example, but it does control a space that wide. (Ibid, bold added)

So precisely how tall a "creature's space" is may be different than its height. Different DMs may decide this differently (declaring a 5 foot cube to be every medium creature's "space" or determining space based on height, or however they wish). In some games, the top 5 foot cube of the door might be considered outside of an enemy creature's space (although definitely within their reach, and thus subject to opportunity attacks).

In your campaign, it looks like the DM considers the top part of the door to be within the hostile creature's space. Thus, unless they are using the optional "Tumble" rules (DMG, p. 272, which allows you to make a contested Acrobatics [Dex] check as an action or bonus action to move through an enemy's space), you cannot pass through it.