Longing for a connection

I have a recurring desire to connect with a girl friend.  On like a thousand levels.  Almost like I had a sister or something.
The problem is, when I gather enough of myself to reach out and ask someone (and no, I'm not asking them to be my BFF, but just to have coffee, chill over breakfast, whatever), two things happen: 1) I'm turned down, and 2) it's not reciprocated.
Is it really possible that everyone already has a best friend and I'm the odd one out?
I really try not to be whiny or have an attitude of entitlement, but I really want to know.
I am aware that the decisions people make in life lead to where they are...have I made choices that have alienated me?
I also know that sometimes personalities don't click...am I boring, selfish, needy, socially inept?
Does the fact that I'm sitting here asking these questions prove that I'm fundamentally not BFF material?
I'm afraid to ask, because I'm sure I won't believe any answers that are positive about me, and I don't really want anyone to tell me anything negative.
BAHAHA...I'm a mess...or am I?

Could it be that I'm reaching out to the wrong people?  What if my real BFF isn't someone I've been striving to connect with?  Oh my...then who IS it?

Or is it just circumstances?  Everyone is busy.

BLAH.  Mind circling. Feeling looney tunes.

Oh, and P.S....anyone who reads this, don't accept any responsibility for this.  It's seepage...not a reflection on anyone else.