Being distinguished is a good thing: it implies good behavior, sharp dress, and an excellent reputation. Distinguished people are respected.
When we say someone is distinguished, we're expressing respect for them. Usually, someone distinguished is older: distinguished people are wise, accomplished, and professional-looking — and usually have an impressive reputation to match. A teenager can't really be distinguished. They're too young to look the part, and they haven't done enough to earn the title. We admire people who are distinguished.