Oh, that doesn't sound good at all. Let me rephrase: all writers need to kill a piece of their own fiction. That's better. See? It sounds so much nicer when people aren't the victims.
I was going through some old papers yesterday and I realized that I still had the old alien invasion novel that I poured so much time and energy into only to see it end without the glory of a publisher. I don't know why I held on to the hard copy of the drafts or the files of it I had on my computer. It might have been, in part, because I spend a semester at grad school working on it, refining and raising it to a higher level of existence; I didn't want to see it destroyed.
Then, I took the drafts of their binders and started shredding them. The notes too.
There's more to this than the mere clearing of space. Keeping a failed novel is like hanging out with an ex-girlfriend while trying to move on with your new girlfriend; you're subconsciously tempted to repeat past mistakes. And with every new one, you'll compare them to the old one. I'm back to talking about books, by the way, not women.
So if you have a piece of writing that never quite worked out, get and destroy it. I mean, physically destroy it. That finality is an indication that you're ready to move on.