My very first serious attempt at writing a story for a competition didn't win. Not winning felt bad--never mind that other stories in the contest were better than mine. When you've created only a single work, all your hopes and dreams and fears are tied up in that single story. When you've only created a single piece of flash fiction to share with the world, you're more likely to realize your fears than your dreams.
To begin with, if you've only written a single story you consider done enough to share, the odds are it isn't very good. It takes experience and--perhaps more importantly--meaningful feedback to improve your writing. Looking back on it, my first story to share was a poor vessel for my hopes and dreams. I'm pretty sure that's the case for everyone.
Improving is no guarantee of success, of course. Most of sending your writing out into the world amounts to seeking rejection, and that rejection comes in a reliable flow of form emails thanking you for your interest, along with the occasional gem actually written by a human and intended for you alone. When you are shiny and new, you haven't realized just how high the ratio of rejection to success really is. Even when your work is good enough, it's far more likely to be rejected than accepted. That's just life, but you don't know that when you start off.
The nifty thing about writing and writing and writing, other than the chance repetition has given me to improve, is that having more stories to send to more places has lowered my emotional investment for each one. I haven't tallied up the number of pieces I am sending around, but there's dozens at some stage of the process. Facing the rejection of 1/36th of the output of my brief literary career feels less scary than rejection of the sum total of my literary career. That I've found a few modest successes along the way helps.
I can't help but be emotionally invested in everything I write. If I'm not emotionally invested, there's just no point in even writing it. Spreading that emotion out, though, makes the inevitable rejection go down better. The initial rejection can't help but hurt. The solution is to write more stories so that you can at least spread the rejection around.