First of all, it’s okay to be jealous and angry. While they’re not “productive” feelings, they’re not wrong either. It’s only wrong to let yourself be consumed by them.
guesswho is right: the people that make the selections for your camp have a different point of view; they may not see the same qualities in you that they see in the selected people. Yes, sometimes those qualities are such highly objective things as “he’s been my best friend since forever!”
If you’re still going to camp, try to find out what the other people brought to the table. As Riser said, asking in a professional way, trying to find out what you can work on do better for next year, is perfectly reasonable. Even though it may be what you really want to say, “those other people suck, I’m better in so many ways, why didn’t you pick meeee?” isn’t going to have the desired effect; it makes the people in charge of selection defensive and it may emphasize some of the less desirable qualities in you that we all have.
If they won’t offer you constructive criticism so you can do better next time, then those people may not be worthy of your attention. That’s when it becomes time to change the way you look at camp and the value you place on being involved with it. Either go because you like going and you get other things out of it, or decide that if you can’t be on staff, you’d rather do something else. It’s a hard choice.
I imagine I’m quite a bit older than you, and I just had to do this process with something that was pretty important to me. The only reason it gets easier as you get older is because you have mor practice at dealing with disappointment.