If you don't establish your copyright though simply creating it won't cut it. If someone steals this work of yours and they publish and establish their copyright on this work, you just lost it (unless you can prove beyond a shadow of a doubt that your work was stolen and that you created it).
Technically yes, if you want to be able to claim copyright you need to establish it in a way that makes it clear that you are the original author. Most of the time this isn't a problem because no one is breaking into your computer to steal your short stories before you post them.
The only time I can think of where this gets hazy is when you grab a story from 4chan. I think in this case it would be hard to argue ownership either way between two parties because of how anonymous the platform is. This is a matter you would probably need a keen lawyer to discern case by case.
I think you also got too hang on my "void the copyright" term. What I obviously meant was that no matter what license Reddit marks your work as, the story is licensed as CC-BY-SA if you post it here, as per the ToS of this site. I didn't mean that you no longer hold the rights to your stories, that wouldn't make sense.
I probably did infer something other than what you meant there.
If you post your story here then you have released it under CC-By-SA and you cannot revoke that. But if you go ahead and post it to reddit as well without acknowledging that it is available under CC-By-SA you are breaking the terms of your own license. But, doing so doesn't change the fact that you already made the content available under CC-By-SA.
I am not sure this is true. I know of authors who have posted their work here and then needed the work published (under a third-party publisher). These authors subsequently deleted their stories from here because they shared the rights to their story with this publisher.