As previous posters have stated, you have to be careful not to confuse arrogance with self-confidence. I seem to have a reputation for being arrogant, but quite frankly I think I'm a mediocre person, academically and socially - I have no inflated ego at all. But just because I have confidence in my opinions and am unafraid to articulate them, and accept compliments when I feel I deserve them, some people construe that as arrogance - which is completely fair and I can understand why, but it's not an accurate representation of me. I wouldn't be surprised if many Oxbridge students were similar - realistic about their merits, but confident in themselves. It seems that people are supposed to put themselves down all the time, and if a person doesn't (but, at the same time, doesn't brag), they can seem rather egotistical.