Even if the rejection is specific to one area of life, it gives me a feeling of overall unworthiness. I've cried over rejection in the past. I've also brushed it off outwardly and then went to drown my sorrows in a cigarette (back in my smoking days), alcohol (back in my drinking days) or food (I still eat, but I've avoided major binges for quite awhile now).
It's not possible to be a writer and avoid rejection. Well known and well published authors are rejected. Stephen King hung his rejection letters on his wall and almost gave up writing when he couldn't publish his first novel. Very few people are charmed enough to lay the golden egg of manuscripts each and every time they attempt it, and even small rejections can be painful.
Most of my submissions to Associated Content over the past few years have been accepted, but a several have been rejected for upfront payment, and a couple have been outright deemed unworthy for publication. It stings to know that something you thought it was good didn't make the cut. It's not easy to hear your work wasn't good enough ("I'm never writing again" mini tantrums have happened, though I'm ashamed to admit it).
I've grown a thicker skin and I've even learned to find the upside of rejection. Articles that don't make the cut with AC give me something to send to a different platform or give me a blog post I didn't already have. Rejections of larger projects generally come with feedback to help me improve my writing. You can't get rejected if you don't try something new and put yourself out there, so I've managed to even take pride in some of my rejections.
Most recently, I applied to be a movie writer for a gaming site. During the application process, I was really excited about applying and really wanted the job. I didn't get it. The rejection was very nice...the writing was good, they were just looking for someone with more experience. I had a moment of disappointment, but I avoided the whole "I'm not good enough to be a writer" scenario. To be honest, I felt relief, realizing only in hindsight that I may have taken on a little more than I could handle.
That's not to say I won't keep trying. It's in my nature to overschedule and deal with the consequences later. But I've managed to change my thinking to look at the brightside of the word "no."
Heck, someday I might even frame my rejection letters and hang them on my wall.