These keys are made for sharping

I keep thinking about something a bassoon teacher once said: keys are on (woodwind) instruments to raise a pitch, not to lower it.

Think about that for a moment.

I don't mean the pads or levers that close and cover the tone holes, as they are clearly meant to lower the pitch of the tube (sequentially cover all of the tone holes on a clarinet, and the pitch goes down); long tubes make lower pitches.  Basic physics kind of stuff.

But the keys that don't cover the main tone holes are where they are to allow the player to play all of those chromatic notes that the basic instrument could not play if it only had the tone holes.  For example: the Eb key on the right hand side of a clarinet (and operated by the right hand first finger) is used to raise the already fingered note D one half step.  We refer to the key as an Eb (E flat) key, but in reality, it is raising the D to a D# (D sharp).

It's the same story an octave up (still on a clarinet) to the Eb/D# key on the right hand (operated by the right hand pinkie finger).  To play the note, the clarinetist must cover the tone holes for D, they open the Eb key to raise the pitch by one half step: to D#.

This is profoundly simple, but I think it isn't recognized right away because we often refer to those keys in their enharmonic flat names.  There are a few anomalies, like the G# keys on saxophones and flutes, but their half-step-raising-D mechanisms are still usually referred to as Eb keys.