The study of literary theory is several degrees removed from the process of writing literature. The discipline incorporates elements of political theory, art theory, and cultural anthropology; its great works are often dense and dry. Studying Edmund Burke or Louis Althusser will not give you any hints on how to improve your sentence structure or tighten your plots. Nonetheless, some writers find it rewarding now and then to devote a little attention to literary theory.
This discipline is not concerned with the crafting of a work, but with the reading of a work. Literary critics explore the relationship between a story and its reader, and they do so from a variety of angles. There are critics who want to examine the nature of beauty; there are critics who want to examine the representational nature of language; there are critics who want to examine the subversive politics that make a certain narrative appealing.
Because the practice of literary criticism is so reader-focused, I find that reading criticism helps me understand why the audience wants the things it wants. This in turn helps me think of ideas that a particular audience might enjoy. An interesting discussion on a topic might inspire me to take it up in a story, or a harsh criticism of a trope may inspire me to re-imagine it in a way that makes it more palatable.
I certainly won’t argue that reading criticism is a necessary exercise for everybody; in fact, I seldom find I have the dedication to read a dense critical piece in my spare time. However, writers who have a high tolerance for dense prose may find some remarkably good ideas buried in a piece of literary criticism.