Most writing intended for publication is failed in the sense that most of this writing will not be published. (Though the proliferation of online magazines is changing the proportions somewhat.)
Most writers will fail in the sense that they (we) will not be as successful, rich, famous, admired as they (we) hoped, or may not be successful at all at any point in their lives.
I spend most of my day, at school and in Uncanny Valley and at other lit blogs, negotiating the terms under which these writers and writing (and my writing) will fail. For every hundred stories I read for Puerto del Sol, less than one gets in -- and my odds, given my placement in the organizational chart, of seeing any successful prose piece before publication are 100%. Some readers for Puerto very likely see zero published pieces in a given year before we print the magazine. Uncanny Valley has an unusually high acceptance rate mainly because we have been unusually good at getting word out to, and interest from, writers we already admired or have come to admire. In workshop we discuss how best to revise a story with the usually-unstated goal of publication, which most stories we workshop are plainly unlikely to ever achieve, though the number that manage is higher than zero, though not by much. (Poets are a somewhat different story, of course, at least at NMSU.) When I teach I am discussing works with undergraduate students whose odds of ever finding publication are genuinely close to zero.
As an editor I often find myself rejecting a submission from a well-meaning, hard-working person who has probably been rejected hundreds of times already, who will likely spend the rest of his or her life as a writer seeing only rejection.
Even a successful writer (in the sense of publishing a high percentage of one's output in the sort of publications one admires, apart from any financial or career concerns) will spend most of his or her time failing: a piece is usually, but not always, rejected many times before it is taken. Rejection is in any case by far the most common experience to follow a submission. Writers develop the ability to satisfy themselves with kind rejections in lieu of acceptance.
What are the implications of these facts? If you call yourself a writer, how do you live with them?