They are in fact teenagers by the modern definitions. You were a full responsible adult shortly after puberty. Many of the greats did their best work before 20.
Much of low life expectency comes from very high infant mortality -- deaths to age 5 or 10. Once you've passed that threshold, your odds of survival increase markedly. Perhaps slightly lower than today's first-world standards, but hale-and-hearty at 15 doesn't mean you're going to fall over dead at 25.
You also want to look at life expectency at any given age. And I distantly recall that the number of (I can't remember specifically which) Greeks or Romans surviving to age 80+ compared favourably to modern times.
I remember reading stories where he charged ahead of the rest of the army, scaled enemy walls, chased down royal bodyguards and so on. He was bloody crazy. A guy with his (lack of) brains should not have made it past 16, let alone get to 32.