The reason they are unwilling to give reasons is because they don't want to have to deal with students disagreeing with them. I'm sure for every valid complaint, there would be many more invalid ones. It's rubbish to be on the receiving end but that's a flaw with the amount of people applying compared to the places. Remember for Oxbridge, up to half the places may be going to international students as well. Well the students at Oxford do their best to alienate everyone around them