I like writing because I have stories I want to tell. Stories that have to be told. Stories I want to read. Stories I want to share. To me, storytelling is the ultimate form of freedom.
I enjoy creating stuff in a lot of forms, but writing is one of my favourite ways to create because it's super fun to explore what makes your characters tick and how that has influence on the story and your other characters. You can do that in drawing, rp'ing, etc. too, but writing is one of the easiest ways for me.
I wrote a short story in the second grade. I also wrote poetry, one of which impressed the adults. Can't recall what the actual impetus was. Creativity and mental focus are things I've always reached for. I'm a 'what-iffer' and will often have stories play through my thoughts when I lay down to sleep. I wanted to be a writer at an early age, then life got in the way. I finally came back to it in the 80s, writing a series of apologetics that stemmed from focused studies. In the 90s, I wrote another short story, and I began work on my first novel. It's like this: a dancer needs to dance, a singer needs to sing, and a writer needs to write.
It's extremely cathartic to see ideas actualized, otherwise they just bounce around in my head until I get them down on paper.
I was writing stories, beore I could write. In my head, whatever I was putting on paper was a story... It was mostly drawings though. Writing is an escape from reality, you get to be very creative and create a world of your very own. My bonus is that I'm an artist as well. So, I get to combine both. If I want to relax, I either write or draw. Both put me in a zen mode.
Writing just amounts to expressing my feelings about the world and creating a fun narrative with them. It's also a self-discovery thing. Some people might find my work boring because my characters talk and argue a lot, but in some cases it's really just me trying to think more on things and define the way I feel.
In short, sometimes it's hard for me to vocalize how I feel, and writing helps to that end.
Catharsis! One hundred percent! Like a scratch that I really need to itch. A lot of times the characters are going through the same things I am.
Escapism! Daydreaming about characters, worlds, events, and so-on keeps me amused. It's like having my favourite movies on-tap in my brain 24/7. Writing them down or drawing them allows me to share them with others and makes them that little bit more 'real'.
Like a lot of people, I have stories in my head and I want to share them. My biggest drive lately is my desire to have my work put on the screen. Some of my family aren't big to sit down and read a 20K novella but they're pretty good to watch an hour long TV show. I want to share my work with them too.
The money.
Seriously, when you're a freelance writer, right now, you can stop by several sites online and blog, post how-tos, recipes, reviews, etc. etc., and get paid for it.
We possibly like writing too because we're so bloody good at it, and our dreams of joining a circus didn't pan out.
When I was a kid I used to just love writing because it felt good to put my ideas and thoughts on paper. After getting praise from teachers and friends from it, in high school I just kept it up to impress people tbh. Then after highschool it was right back to doing it because it felt good. NOW its a combination of that and the money motivator.
honestly it's because too many ideas bounce around in my head, if i don't write 'em down, i start getting a headache. though that's probably just me lol. it's also fun to come up with characters and worlds.
I like writing because I can finish a whole story way faster than drawing it out as a comic.
Plus the liberty of creating whatever story I want, expressing myself, etc.
I enjoy writing because while I love drawing too... There is nothing quite like painting a world with your words! 
Without being too graphic I guess, writing literally saved my life. If it weren't for my characters and the worlds I would visit with them, I wouldn't be here. I write because I feel this need to tell their stories because for some reason they chose me to tell them. My friends have likened me to a bard because it is my life's work.
I love reading stories. A lot.
But one day, I ended up reading all of the stories (that i could get my hands on) that had all of my favorite tropes. Or, I read a story where I wish a character was treated differently or acted differently.
Instead of tirelessly finding a story to match my specific taste - I decided to write it instead so I can read it. (Thus a fanfic writer is born)
But, I also enjoy writing. It's a craft I will never master.
I love fantasy but I get frustrated by all the Tolkien clones and thinly veiled DnD campaigns in the genre. So I took matters into my own hands and started writing my own.
I got a lot of ideas in my head, so I write to flush them out.
I love writing character interactions where they just talk. Whether it's to move the plot forward or just killing time, it feels great getting to flesh them out bit by bit. Especially when I get to improvise out of nothing and make something work. Feels good.