You're alone with yourself and your own feelings and that gives you deeper access to what you need to get in touch with to write poetry.
Fiction writers learn about the development of metaphor, the use of rhythm, the way that language is compacted in order to express the feelings of - express their own feelings and the feelings of their characters.
So, some of the most difficult formal poems that I've written, say one sentence sonnets, I've been able to do those fairly quickly whereas some of the clearest, simplest lyrics that I've written have taken me the longest to get to the clarity of feeling that you're looking for.
Sometimes I have a feeling that I just can't get rid of. Sometimes there's an experience that I want to write about that I have to get off my chest. Sometimes there are some words that appeal to you.
And when I'm writing well and when I'm inside the feeling, then I can do fairly complicated things with some fluency.