Well Holy Horcrux, this answer could be really short:
I can't not write kaythxbai.
Or obviously, really long. And since the topic came up from two different sources I'm going to contribute to both, 30 Day Challenge: YOUR DREAM JOB and a Flash Fiction Challenge: WHY I WRITE.
...because I'm a person highly averse to violence, danger and conflict and I very much like to prevent other people from engaging in them too. So if I decided, these characters' lives would basically be just a ridiculously happy-go-lucky family comedy or something.
Anyway, if your head fills and fills with characters and their stories, and you never put those things out, you know what happens? That's right, you go insane. Because the old things will keep replaying and the new stuff will keep coming.
Once I write the stories down, they become solid and my head will stop processing them.
(Of course I will have to process them again when I edit, but that's a completely different thing, because it's a conscious evaluation process.)
Writing eases the noise in my uncontrollably active mind, grants me some time and energy to function like a normal human being again, and everyone is happy. Yay!
So, rather than something I do, writing seems to be something that happens to me. But while I may be somewhat passive by nature, luckily, I'm not passive enough to not take advantage of something that happens naturally, and try to make it into something great, valuable, a life purpose even.
That's why I also have other motivators to write. First of all, I can't just watch people and not care. Whatever their story is, how their mind works, what makes them tick, nothing interests me more while I'm faced with them. I want to understand them and help them understand themselves to be able to solve their problems. And I don't doubt that the fictional people living in my head reflect the people and problems I've faced. However, they do not do it directly. They're more like a side effect of the developement of my theory of mind, an unconscious construct of the knowledge I gather.
That being said, I realise how stupid it sounds to call my stories ”a side effect” since they're easily a priority to me. But I only mean that in the sense that while I think of writing as something I was ”born to do”, real people are the source of my inspiration and the only thing that ultimately can give my writing any value. Ideally, they will affect my writing and my writing will affect them.
Which brings me to another reason why I write. I enjoy reading immensely. And naturally it was because of other people's books that I realised there was no other profession in the world I'd want to do rather than be an author.
I think reading is just a really great hobby in so many ways, but what I appreaciate the most about it is when it makes people both, feel understood and understand other people better. Ultimately, for me, reading is entertainment but that surely doesn't mean it's not useful outside itself. And no feeling compares to being able to give that entertainment to others. I'm not a published author yet, so the circle of people who have read my stories is small, but I'm pretty sure that without the experience of them enjoying it, my stories would never go beyond first drafts.
So yeah, while I think I write because I can't not, and I write what interests me, making no compromises, I also think that my writing wouldn't have any meaning if it wasn't about other people and for other people as much as it is for me.
Like reading, writing is also plain fun. While the stories just come to me and while there are kinda sorta humane idealistic motivations(=excuses) to pursuing a writing career, the craft itself gives me a sense of creativity and freedom no other medium does. (Drawing comes close, but I don't think I'm as good at it, so...) I may not feel like I'm in control of what I write but I very much feel I am in control of how I write it and I enjoy that feeling.
I decide which qualities and details I bring out in the characters, places and scenes. I recreate the atmosphere, I balance out my vision. It's bound to be different than what I actually saw in my head but that doesn't bother me in the slightest because that's how I control the contrasts of the story. It's up to me whether the story is supposed to come to the reader in HD screen, or like a distant memory, or something you're hearing from a friend. I think there's a place for any variation and I want to get better at writing to bring out the best in the stories that fill my head.
So, I also write because of that. Because the actual deciding which words to put on the paper/screen is fun and it makes me feel present in the story, like I'm interacting with my characters. (Especially when I write in my preferred viewpoint, omniscient.)
Those are probably the main reasons why I write, and want to be a published author...
So yeah, I don't really have anything cheesy to check out with. :D