Preface: This does not, as I believe some authors* have misinterpreted, mean "kill your/everyone's favorite character." It means that a writer will sometimes concoct a sentence (or paragraph, page, etc) that reads like pure gold, but just doesn't fit the story, no matter how many times/ways you try to make it work. (i.e. it's depressing as all get-out.)
This is the most difficult thing about being a writer. Any kind of writer. Yes, there are days where you may think woe-is-me, it's so hard to get going or woe-is-me, this chapter is not my finest work, but when you write something you think is positively brilliant (I'm talking it-practically-knocks-you-out, Wow-I-can't-believe-that-came-out-of-me brilliant), you will fight yourself near to death when faced with cutting it. If you've never felt this way--if you've never had to almost literally^ beat yourself into submission over this problem--there are two possibilities: 1. There was a time when you didn't cut something you should have or 2. You've never written anything.
I'm encountering this problem now. I have this short story I wrote, but in looking it over to consider a re-write, I'm faltering. Originally, I was going to start it over from as close to the end as I could get it (per advice from the genius-and-deceased Kurt Vonnegut Jr.) because the current story spans about twenty years in about twelve pages (though, arguably, it was pretty seamless, considering). I would still like to start from the end of the action and try to contain it all in a short timespan, but the beginning of the story is so good. All of the back story is friggin' awesome--it tastes like something I wrote. So goshfreakingdarnit, I don't want to scrap it. But I haaaaaaave** to. And yes, it will still live on a word doc full of other little darlings that I half-hope will eventually have new stories to house them--but that's pretty much wishful thinking. Rarely do you look back at the amazing sentences you wrote for other things and say "Hey there! You'd fit perfectly in this other story!" (especially without further prodding, trimming, and general squishing like the proverbial square peg in a round hole).
On a positive note, this whole dilemma signifies that I am fully capable of creating darlings that necessitate killing, and that gives me some nice warm fuzzies. WRITING IS TOTALLY AWESOME I FEEL SO GOOD ABOUT IT ALL OF THE TIME SO THERE. ...Sigh. Even work you love is hard.
^CLARIFICATION:
I mean literally. As in actually punching yourself in the face, hitting yourself with a bat, what have you.
* cough*JKRowling*cough
** this is me whining