What makes a writer 'what', you might ask.
What makes a writer tick? Swallowing a watch will do it. But be warned, the battery acid's no friend to your taste buds... yes I know this from experience. And no, I won't give you details.
What makes a writer cringe? Usually the word "Oops" uttered with any proximity to their writer-nest (yes, writers nest. We're worse than birds for trenching in.)
What makes a writer tear their hair out? Usually "Oops" followed by the screen going black - just as they were about to hit "save" after 3 hours of brilliance wherein they didn't save once.
What makes a writer want to eviscerate someone with their pen? (And by "eviscerate", I -of course- mean literary evisceration where the offender lands a staring role in the writer's next tragedy.) Finishing a book only to read their blurb on the back of one already published or in the review column for a movie.
There's a lot of ways to answer "What makes a writer" depending on how you end the question. For the sake of this post, I'll stick to a broad interpretation of what characteristics make up a writer's personality.
Traditionally, writers fit into the "loner" category. Maybe not total recluses, but writing for any extended period of time requires moments of solitude. We need quiet so those voices no one else can hear have a chance to speak. If they can't speak, we can't hear them, and then we can't tell their stories.
Writers can be moody. We get angry or elated because we're creating experiences that no one else is a part of. They happen in our heads and hearts and spill out onto our pages, but explaining that can be awkward.
Writers are actors and directors. We control the action (the characters control it, but let's pretend we control them, okay?); we set the scene. We're every member of a production crew in front of and behind the camera. We're every character and every voice, and as much as we may not like it, all of their flaws come from us as much as their triumphs.
Writers are dreamers. The first stages of writing a shiny new WIP involving sitting and thinking. This is usually the point someone thinks we're not doing anything at all and wants to either take possession of the computer or start a conversation - neither of which makes step 1 any easier.
Writers are under-appreciated. There's a semi-famous story of Louis B. Meyer (from M-G-M), who had a horrible opinion of the writers who wrote his iconic films. He didn't see the need for paid writers because in his opinion, directors and actors made the films, not the writers. This was back during the contract player days when the studios were mini-empires and no one dared speak against the emperor. That comment was the last straw for one particular writer. When the time came to hand in his next piece, he delivered a stack of blank pages to Louis and (paraphrased to remove a few colorful adjectives/anatomically impossible suggestions) told him to knock himself out.
Writers exist in a state of optimistic pessimism. There's a strange mix of hope, confidence, and self-doubt that ebbs and flows during the writing process. I wonder if writing is what set Ben Franklin's opinion that one should "Hope for the best, but expect the worst. If it doesn't happen, you'll be pleasantly surprised."