Empty

[RiverNotch]

You fall asleep in her arms, but never in mine
You tell her how you feel, but to me you're always fine
For a while I could not accept your denial of my importance in your life Way too long, way too abstract, and the rhythm is a clean break from everything else. This line runs like prose, not poetry.
But I was the one who was wrong to begin with The lack of punctuation becomes obvious here. There's no clear continuance between everything, so this loss seems ill-reasoned, and thus detracting. Remember your dots.
I believed there was something between us
Something that I've only ever caught a glimpse of "That" spoils the rhythm, or perhaps the whole line's rhythm is itself spoiled. On rhythm: you have something close here to iambic. Since you're talking about something rather soft yet passionate, to go entirely with iambs would be best, I suggest.
And I had hope for us
I had hoped we would grow, together as people The comma is unneeded.
Wrong was I, wrong was I I agree with an earlier critique here. The inversions here are very out of place. 
Not that you are not fit for me 
But I am not fit for you  The break in the rhythm in these two lines feels appropriate, because of the intensification of thought, but the break would be stronger if you went all out iambic earlier.
Only because I am not fit for anyone
As a heart that's never been whole can never truly love The sparseness here begins to border on blandness. We get it, you feel sad and empty, but you don't really show anything with it. [I keep returning to the same examples here, but I suppose my reading's not as wide as it could be yet when it comes to number of authors, and this woman's work really is one of the best examples in the business, but] stuff from Louise Gluck that deals with this sort of stuff has the capacity to echo the same level of emptiness either with novelty (good), with actual thought [behind the emptiness] (better), or with actual meaning [so too behind] (best: as in, one cannot know light without the darkness, one cannot know matter without space). 
But I do not feel sad to see you with anyone else And here, the line is crossed.
I do not feel sad
I do not feel anything at all 
I am empty
Overall, trite. You have a good sense of rhythm, though: if you're a good orator, a fair bit of tweaking, and this'd be good for a slam. Good, but not great: again, trite, empty in a stupid way.