When playing a brass instrument, on a given harmonic, you can bend the pitch above (to a higher pitch) and below (to a lower pitch) where it sounds the best (while staying on the same harmonic, with the same length of tubing, i.e not changing fingering if playing trumpet or lengthening the slide on a trombone). However, it is much easier to bend the pitch below than it is to bend above. Also, you can bend the pitch a lot lower than you can bend it higher. You can bend the pitch almost down to the pitch of the harmonic below it, but you can even get close to bending the pitch up to almost the harmonic above it. For example, if playing a middle F on a trombone, you can bend it down to almost a Bb (the note of the harmonic below the F), without moving the slide, but when bending up, you can't get even close to the next harmonic (also a Bb) above it.
So my question is: why is it easier, and why is there more room, to bend a pitch below where it rings the best than it is to bend above?