Flute and woodwinds in general are more problematic for tuning as it is harder to "bend" the pitch as
@MRC01 described so well. Strings can adjust their finger placement to change the pitch, and brass players can adjust our embouchure ("lips") as well as move slides. Trombones are just one big slide, while trumpets and french horns have various moveable slides to help us stay in tune, some with rings or triggers to adjust them on the fly.
Tuning needs to be adjusted constantly to suit the chord structure as well as things like changes in temperature and humidity. To make a chord sound good the third needs to be flat and fifth high in a major chord; for a C chord, the E needs to be flat and the G sharp to get the overtone series to line up nicely. Temperature is a biggie; brass and strings go different directions with temperature. But humidity and temperature are both first-order parameters in the speed of sound and thus pitch. Pressure is another; I have to tweak things a little differently at home in the mountains vs. at sea level. The better a group plays in tune, the better (richer, fuller, bigger) the sound of the ensemble.
There are trumpets that have slides marked for A=442 and A=440 (nominal) but 2 Hz is not a huge shift (but is very noticeable if you're used to 440 Hz tuning). Other factors can cause that much of a shift. 432 Hz is a rather significant change.
It is actually often harder to play with a piano or other equal-tempered instrument as you can't adjust for chords and such. Pianos typically use multiple strings per key and "detune" the other strings to help with tuning plus enrich the sound. Pianos also tend to have their octaves expanded, going a little further "out" in pitch at the extremes of the keyboard. Again, makes it sound better, but harder to to stay in tune with it. My wife plays piano (keyboard, organ) and we have done a fair number of duets, so it is something I've been dealing with "forever", like most musicians. Same thing happens when a piano or keyboard is added to an orchestra or band.
Relative pitch, the ability to hear and stay in tune, is a requirement for s musician (and hopefully a singer). But after a couple of decades of playing a Bb horn, switching to C messed me up badly when I first did it (about 20 years ago now, time flies) because my brain "knew" the pitch for the note on the page and it was a step lower than what came out the bell. Now I have a bunch of different trumpets in different keys so I can mess myself up all kinds of ways.
FWIWFM - Don