The trumpet is heralded as one of the hardest band instruments to learn. This reputation comes from a variety of things that influence how you play the instrument. The hardest thing to learn isn’t the fingerings or how to hold the instrument when you play it. The hardest thing to learn is how to blow into the mouthpiece properly, or the embouchure. This is typically the first thing a beginner is taught how to do since it is so important to being able to play the pieces right.
If you are able to make the right embouchure on the trumpet, then you learn how to finger and make the different notes. Arguably, the hardest part of this is knowing when to tighten and loosen your lips to make the various pitches, since the slides are stationary when the instrument is played.