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.
As Toni Morrison once said, "If there's a book you want to read, but it doesn't exist, you must be the one to write it." These days, it seems there are a LOT of books I want to read that don't exist.
There are three main reasons why I write... But i'll warn you before you look down...
My opnion might be a bit of a downer, and depressing... So please don't take it the wrong way, and maybe, don't read this if you're a depressing and anxious grape like me.
1 - I got a boat load of ideas... Like all the time... I need a creative outlet to let that flow out of me, otherwise it piles up and even stresses me to some end, i'm always doing something creative, writing, playing tabletop rpgs, Designing tabletop rpgs and other stuff. So yeah, this is the chillest reason.
2 - My story is a thing only I can do... Sure, someone else might be able to get 'the general gist' of it, and pick up for me, but I am the ONLY PERSON IN THE WORLD who can do it the exact way I'm doing it right now. So it gives me a sense of purpose,
I love these characters they quite literally save my life at a point I was at my lowest, and i want them to do the same for other people... And the only way I can do it right now is through writing. So I do it because it is essentialy my life goal.
3 - And this is the real downer, so take care while reading...
I want to leave something positive behind when I am inevitably passing off this life.
I struggled a lot with the thought of death to the point i couldn't bear to live anymore... And it was these characters that saved me from that, they made me realize as I dreamt of their adventures and life, that there is more to life than effectiveness and a dry sense of acomplishment that comes from working 8 hours a day all week to feed the system.
They helped me appreciate the little things of my life, to learn to chill and smell the flowers, and as bonus... This story was what connected me to my husband (he was my first reader ever),
So yeah, i have a lot to thank this story for, and maybe, a hidden fourth reason, the fact that the only way I can show gratitude to my boys is to tell their tale, and hope others will listen ^^.
I think that feeling of existential crisis exist for everyone in some form or another. I read your post and I HAD to reply because I relate to your feeling of coming home after a 8 hour shift of mundane reality and it's just .... draining. The thought of the after life or perhaps lack thereof also frightens me at times. Leaving something positive isn't depressing at all. Everyone wants to leave a mark in some way or another I think - to say - "I existed! I was here! I was important to someone!"
The idea that even one person would read what you left behind is proof that you existed and your life wasn't just for the sake of living. 
