It's about meaninglessness. Maybe it's just me, but things (including life) that are finite are valuable and special for me. Also in terms of Lord of the Rings I would rather be a human or hobbit instead of an elf. But I respect elves and get your point, it's just not for me.
Eternity is an overwhelming concept. It's easier to tackle it through mathematical induction.
Can you imagine a day in which you feel so fulfilled, so bored, that you say to yourself, "it's enough"; a day in which you wouldn't be interested in what tomorrow will bring? I can't. Hence, by induction, I'd prefer immortality.
I'm probably not going to change your mind, just sharing the elvish perspective.
(And in terms of boredom, because I'm guessing that's what you allude to by invoking Q: you can always decide to end your existence after you get bored with eternal life.)