Note too how he tells everybody about the Brom thing as if he were showing off his new skateboard. Discovering his father's true identity should be incredibly painful and confusing and he should be working through a lot of complicated emotions about it. Instead of which he treats it like something to brag about. Which pretty well reinforces what I said in an earlier chapter about how Brom being his dad is just another Hero Accessory when all is said and done. Because that's exactly how it's treated by the narrative. And Eragon immediately forgets all about it up until the point where he gets an opportunity to flaunt it to make himself look cool in front of his would-be girlfriend. This is Grade A Dick Behaviour and in a sensible novel would have been greeted with funny looks followed by contempt.