It seems to me that Eragon is dangerously idealistic given his reactions to Torkenbrand's death, and Arya making sure that the soldiers of the Empire they killed after he killed the Ra'zac, looked like they had been killed by humans.
I have. Teenagers just can’t empathize like adults. It’s just not possible. Their minds are going through such drastic changes, they are not able to think “reasonably” so to speak. Couple this with the crushing amount of stress Eragon is under. It becomes very understandable.
We have to remember that culture and personal factors can affect how arrogant someone is. Eragon was not only quite young(and young people are usually quite idealistic), but he’s also from a culture that quite values their pride. There’s also Eragon’s personality. He’s quite adamant about his beliefs(at least at this point in time), and a bit of a do-this-first-afterthought-later type.
The only really proud person in Palancar Valley were Garrow and his sister Selena. I think Garrow's pride rubbed off on his son and nephew. But you do have a point about Eragon's personality, very adamant about his beliefs and a do-this-first-after-thought-later attitude. But what really struck me as arrogant about Eragon, was how demanding he was when asking questions.