Because it's just something I do, it just doesn't occur to me that not everyone can or has separated themselves from their work. If you read my post "the best ass-kicking I ever got" you know there was a time I wasn't so amicably separated. I have since learned how important it is to separate myself from my writing. It's probably one of the most important things I ever did as a writer.
It's scary to think about sending our writing out into the world to be judged. It hurts to be rejected, or to get feedback that tells us our stories need more work, even a didn't grab in a technically good piece. Writing is an intimate act between you and your words. It's like the joy of your first kiss. Sending it out is discovering that your mom was hiding behind the curtain videoing the whole thing, and now plans to show it to everyone you know. It's not yours alone anymore. It belongs to everyone your freaky mother decides to show it to. The same goes for your story. Once it's out there, it can't be intimate anymore. It's not just YOURS. And it will garner all sorts of reactions; some you might be uncomfortable with. Some that might hurt. Some that will fill you with joy. It's what happens. No way around it.
If you separate yourself from the work, it gives you perspective for both the praise and for the criticism. If you can look at it as something outside of yourself, you can process the good and the bad feedback without letting it go to head or heart. It's not you. It's not your "baby." It's a piece of writing. It represents itself. Not future work. Not past work. And certainly not you as a person.
Fear isn't being nervous about sending something out; it's that thing that keeps you from submitting your work entirely. If it comes back with a definite needs improvement, so be it. No one is making a judgement call on you or your talent, only that piece of writing at this time. If you trust the judgement of the person behind the criticism, you must accept that there is something to it. You can listen to that criticism with an open ear and improve those things found lacking, or you can wallow in despair and never write again; or you can say, "this person knows nothing!" and send it out again to be likewise rejected.
Separate yourself from your work. Feel the joy of your accomplishments, but the flip side of that is not suffering your failures, it's accepting them, learning from them, and letting them go. It hurts only as much and as long as you allow it to.