Writers realize that there are other people who can write an extremely well-structured, gripping novel in a matter of months. Artists see their colleagues do live drawing and suddenly understand that something that is painful and difficult for them comes easy for these other people. (I don't have musical talent, but I expect something similar happens there.)
Are they geniuses? Probably some are, but mostly they have just worked very hard and built a set of habits that lets them approach creative problems with that seeming ease.
Making software is really primarily a creative pursuit like these others -- it just has a bit more math and a bunch more high-tolerance engineering thrown in.
Personally I think of programming as a cross between architecture and writing: I'm making something that has a visual presence and which end users can "live in" or "visit" (very much like a building), but it's also a story because the interactive medium necessarily imposes a narrative. This way of thinking helps me figure out the elements that go into software products... But probably everybody must find their own metaphors to make sense of what they want to do in this field.