The former makes some amount of sense: teenagers are just starting into the world. And there's a bit of a cycle here, because people who are worried about teens getting hurt tend to try and stop them from doing dangerous things. But we learn to do things by doing them, so that can just end up meaning that we step into the world and do all the dangerous things a few thousand miles from home, without a safety net to catch us. There's a lot of room for a self-fulfilling prophecy here.
And, of course, those cool things that aren't worth the risk...they are all new to us. Life is awesome. Remember being young and just-free? The risks may not be lower--though we heal pretty quickly, so sometimes they are--but the rewards are higher. Ask any economist, higher benefit is functionally identical to lower cost.
The answer to the second also sheds some light on the first. We're teenagers. To people younger than our peer group, we are the cool older kids. To people older than that, we are immortal.
Immortal doesn't mean, 'living forever', or even, 'living a really long time'. Break down the word, and you'll get, 'not', 'dead', and 'this word is an adjective'. Immortal means deathless, undying. We will probably outlive our parents--and certainly no one wants to think about us not doing so. Our not being immortal is an awful thought, one people do not want to think.
And, by that marker, it's mostly true. Even in places with high infant and child mortality rates, teenagers don't tend to die. We are hitting our prime. Unless the mortality rate is made artificially higher*, we don't tend to die as much as any other group. We may not be totally deathless, but we do tend to die less.
In summary: teenagers have reason to think they're immortal--and even if they don't know them, other people do, and that affects our self-image.
* e.g. all the teens get sent off to war