My theory has always been that the elves really were immortal, or at least lived for a loooong time. But they were slow. Really slow. Like, "I'm gonna go take a quick nap, see you in three years" -slow.
And the humans weren't.
And then maybe some elf noble went, "Hey these guys talk way too fast, I can barely understand them." And made a spell to speed himself up, and the spell got really popular until elves started dying early. And while everyone was panicking about that and trying to fix it, the Tevinter attacked and enslaved everyone.
Cue thousands of years later and no one remembers the spell, only that they started aging real quick when they started interacting more with the humans.
Or maybe the quickening was a real disease and the elves noticed in time and stayed away from the humans. But then the Tevinter came, and they were just so fast the elves just got run over... And so everyone got the quickening disease because they were forced to hang around humans all the time.
Like, I always figured they were the stereotypical high elves. Slow, peaceful, friends with animals, big wooden house-castles in the forest. And then humans came and were human. But the elves didn't have some mystical defence, and there weren't any orks or goblins for the ancient elves to practice fighting on.