Obviously, Harry Potter and the Order of the Phoenix is a novel about a school. So 99.9% of the characters are very young. The thematic significance of youth in Book 5 isn't limited to the simple fact that the characters are kids. What's more important is that a lot of Harry's troubles spring from his age. He is old enough to want to take control of his own life, but he is too young to be considered an adult in the wizarding world (where the age of maturity is seventeen). Harry is frustrated at the contradiction that he's faced-off with Voldemort numerous times, but he still gets stuck with the stupid Dursleys over his summer break.
Harry's age also means that a lot of people don't take him seriously: Mrs. Weasley tries to exclude him from all Order business. And as for Professor Umbridge, she would probably treat him like an actual baby if she had the chance. She is utterly condescending and disrespectful. This kind of treatment, whether well-meaning (Mrs. Weasley) or evil (Professor Umbridge) infuriates Harry because it reminds him that he is not yet in control of his own life. That's what stinks about late adolescence: you feel ready to take on the world, but the world doesn't think you're ready for it.