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I don't consider myself an accomplished essayist, I can write them just fine, but they aren't anything spectacular. I'd love it if they were, but I never have anything particularly interesting to say about the works we write about. And if the writer isn't excited about what they're writing about, chances are that the reader isn't either. I think the purpose of literary analysis is to have a fuller understanding of the work (novel, play, etc). To put your own spin on the work--what you got out of it, something that maybe another person didn't.
Challenges for me include having a unique point of view that I'm comfortable with writing an entire essay on. Some of my ideas I don't trust, or want to put effort into making it make sense to others. Which, yes, is terribly lazy of me. I put a lot of thought into my Romeo and Juliet essay, but I have doubts that I'll recieve all 100%. My last essays have been in the B range, but I'm fixing my essay tomorrow in accordance to why the last ones lost points.