Ok, so I guess that by "young" I mean "naive" and that he hasn't really figured out what his status really is as a dragon rider.
Eragon gets his fortune told by the awesome witch, Angela. The first thing she tells him is that he will live either a very long life, or forever. His response?
"No surprises there -- I am a Rider, thought Eragon. Was Angela only going to tell him things he already knew?" (204)
But the fact that he's a rider doesn't automatically mean that he's going to have a long life. It's true that at this point he hasn't joined the Varden and that he hasn't committed his life to killing Galbatorix, but even so, he knows that he has powerful enemies and that Galbatorix would kill him, or would at least make every attempt to kill him, for refusing to join the Empire.
Eragon is one of those youngsters who is convinced that nothing will kill him. It hasn't even occurred to him that he could be killed by his enemies. That, right there, is a bit of naivete.
Then Angela tells Eragon that he will fall in love with a noble woman. Eragon's reaction to that?
"Of noble birth, thought Eragon in surprise. How could that ever happen? I have more standing than the poorest of farmers" (205).
Um, hello Eragon, you're a Dragon Rider. I'm fairly certain that that's plenty enough rank to be considered a good match for a noble woman. The fact that this fact hasn't occurred to him is another indication of naivete and some cluelessness about just what his new status is.
Last, Angela tells Eragon that a member of his family will betray him, and Eragon immediately protests that his cousin Roran would never betray him. It doesn't even occur to him that he might have other family through his mother (like, um, an older half brother?) who might pop up in his life in the near future and befriend him. And what about his father? He doesn't know who his father is (despite traveling with him!) and for all he knows he could have a large extended family on his father's side that he'll run into.
The fact that Eragon hasn't even considered that he might have family who he hasn't met is another bit of naivete and cluelessness.
Eragon has some way to go before he becomes a properly mature adult who knows his place in the world and before also understanding some of the harsh realities of the world, such as the fact that it isn't a given that he'll live to a ripe old age.