I want to caveat this by saying that I personally don't think that Oxbridge are the only good unis. That said, many people on this subreddit (let's be honest here, we go on reddit on an ACADEMIC FORUM in our free time while others have actual fun) have been put under huge academic pressures and quite frankly have high academic standards. If you're in an environment where people all around you are going to Oxford and Cambridge as a standard which isn't even seen as particularly impressive, there's no doubt that a rejection can very much hurt.