Any therapist who wants only easy clients, or attractive clients, or articulate clients, or ones who dress well and smell good and would be ideal hip friends or whatever, shouldn't be in the field!
I agree, there's no client who's so intractable that no therapist would want them. It is hard to find good therapists, though (boy, is that clear from this board) -- but it doesn't mean they're not out there. (Or so I keep telling myself

)
Lauren Slater is a psychologist and writer who writes incredibly movingly about these things. In one of her pieces (some are anthologized in the Best American Essays series) she talks about a breakthrough with a really tough case, a prison inmate who hated women and said so. As therapy progressed, each of them made inner discoveries, and ultimately he was weeping in her arms. Gosh, I need to read that again!
Anyway, if you're feeling rejected, that sucks! We expect acceptance from therapists more than from any other kind of person. They're sort of like priests. Their attitude should be: nothing human is foreign to me. They're supposed to be able to identify with their clients, no matter how the externals of the other person's life might differ. The need to be seen and heard and understood is universal, and that's partly what they're trained in.
Long way of saying -- if a therapist rejects you, it's not you. Not all of them are competent. Or their style of relating might be unhelpful. But it's not about you. You can be any way you want to be. It's their job to help you. You're presenting yourself, saying, Look, I know I'm damaged. If a therapist can't handle that, WTF?
That was a big problem for me in my own initial session with my current T. I kept apologizing and saying, I'm sorry I'm not very good at this! He said I didn't have to be!
Therapists have all kinds of standards for what they need to be. Clients don't.