Hi Mr. V.
I have done the same thing, and I actually have had the same thing happen. You get to this point where you're so lonely, and basically just want to hang out with
anyone, and I think other people can sense the desperateness almost, or at least I think I perhaps came off too strong or something. Or I'll get the, "yeah, we should hang out, call me sometime" thing but never get a response from them when I actually call...
BUT, on the flip side: I met a guy in my Physics class once and we had a 10 minute conversation about CALCULUS. He asked if I wanted to "hang out" and I said yeah. HE seemed to mean "date," which I was really not OK with at all. So obviously now I'm a bit more cautious about that, if I don't know the guy very well and he asks to "hang out" right away I might decline even if I really do want close friends.
I wonder HOW she rejected you, did she say something really snotty or seem offended or something?
And I think you're right also that joining an organization or club does not automatically equal friends... which is kind of my problem also: going out and meeting people does not equal friends... The only advice I can give is to keep trying. Most people really are just annoying, and a lot of clubs tend to become very elitist, although it is definitely a good place to start looking for friends. BUT, I also think people tend to have a strong preconceived idea of people who are their type or who they'd like to be friends with. I think this is the worst possible thing that can happen. I mean, obviously if someone feels dangerous or creepy, stay away. But one of the best friends I ever had was a runner/biker/fitness nut while I am... lucky not to trip on the sidewalk. But we both had a love of bad puns so that made conversation hilarious.
I wonder if part of the problem is your expectations. You're in a club. You're in various organizations. Now
where are the friends? This is what you're "supposed" to do, isn't it? ...Yeah. That's pretty much where I am, too. Sorry I don't have more to say. Just keep trying. I won't say that it will 100% guaranteed happen, but the odds are more likely, and what else is life but just a game of chance, anyway? (Much to my chagrin...)