I think one of the most challenging things is composing a complete song. Anyone with any musical experience can come up with a melody and a chord structure to accompany it. However, to get multiple instrument parts to sound good both by themselves and with all the other parts can be frustrating, and certainly complicated.
I am not a good composer. I have really only began composing music on guitar, recording many tracks to overlap each other, and using midi software. It may be easy enough to come upon a pleasing melody, and even a chord progression to harmonize behind it, but to develop these core ideas into complete pieces of music is a laborious process.
I wouldn't be doing it if I didn't love it, though. Just keep this in mind whenever you listen to music: it was most certainly not easy to write the whole piece for whoever did it.