I consider myself an early-adopter. I always try to at least test out new technology, especially if it's what "the kids" are using. But with Snapchat I had a strong reaction of "this is dumb, screw this, I'm too old for this". Plus, no one I knew used it. I guess that makes me old now.
On Snapchat, every picture and chat message self-destructs by default, so there's less social pressure to post something truly extraordinary. There's no publicly visible tracking of likes, so you're not tempted to compare your popularity with others. There is no infinite history where you can come across something old that will make you embarrassed and upset (e.g. records of bad decisions, photos with an ex).
Sending snaps back and forth is great for staying in touch with friends without having to converse about a particular topic. For acquaintances who you don't know as well, an amusing snap is a great icebreaker. And for when you DO want to have a conversation, there's both an IM and a video chat.
The Discover feature where you see content from VIPs directly competes with a significant use-case of Twitter in the target demographic. But unlike Twitter, it's more visual, more immersive, and because of its temporal nature, more exclusive.
Moreover, teens hate creeps. You know every time someone views your snap. You know when someone screenshots your snap. You know when your chat is read. You know when someone views your story. Your audience is exactly who you choose. It's not the internet at large. It's not your mom, it's not the weird guy in your school who found your profile, and it's not people way outside your age-range who are thirst-liking your selfies and making you uncomfortable.