I wasnt really that bothered about rejection, probably because a few years ago it didnt even look like I'd be going to university at all, nevermind being in contention for Oxbridge. I wasnt doing very well at school (I was incredibly lazy, I hated all my teachers, etc, etc) but I sorted myself out and transformed into a straight A student in the space of two years. So I'm just glad to be getting offers for one of the most competitive universities for one of the most difficult subjects.
However, for people who have been constantly told all their lives how clever they are, its probably much more of a shock. I know one guy who I've been to primary school, secondary school and 6th form with that has always been top of the class in EVERYTHING and had always got As. Everyone just assumed he was set for Oxbridge. He was rejected without interview. That must send someone like that crashing down to earth.
To be honest, if getting rejected from Oxbridge is going to be the worst rejection of your life, then you must live a very sheltered life.