Ah, I understand you completely.. and want to offer my support. I also want to offer that they may, in fact, have liked you quite well. And you all must be "good enough" because you were among the FEW who got interviews!
The problem can sometimes lie in very little things beyond your control. Sometimes a program is looking to recruit more males, or one of the top choices has the exact fit in terms of experience, or maybe there is a political connection? My point is, there are a number of factors, and some of them have nothing to do with you or your interview.
You may have seen this in a previous post, but I was a 1st alternate for my first-choice (and only option) program. I actually got a rejection letter after my interview, and spent a whole day believing the game was over. Weeping and all. I happen to know someone in the program, told her about the letter, and she seemed quite surprised and contacted the POI for me. Turns out...I wasn't rejected! BUT, I wasn't accepted either. I was in a holding pattern to see if choice #1 was going to accept. Also, my POI ended up securing funding for 2 positions, so actually that was part of the reason I had to wait. It was at least 2-3 weeks post-interview before I finally got the good news.
So hang in there. I can't promise you that you'll get in. But I can promise that getting this far means you rock. And you just don't know what lies ahead.. it may just be that you haven't found your perfect program yet.