So let me explain it to you this way. And sorry for the condescending sound of it but I really am a pro-life-extension-arrogant-asshole.
Your body seems to be a pretty cool thing. It's been given to you at birth. You even have a mind coming with it which is a different thing and which is actually, on the long run, the only part that really matters.
You have gotten used to identify, during every single of your life, yourself (your mind) with your body to an extent that you have the illusion that the thing, no mater how good or bad it looks like, that you look in a mirror every morning (or even minute of the day if you're a Korean girl, just kidding) is actually an accurate representation of yourself and that it will always be this way.
Hmmm, but here is thing; One of the main reason why you fear immortality even if you deny it is because you are afraid to be stuck, literally with yourself, for the rest of your endless life but this WON'T have to happen unless you really want to (and most probably you won't, trust me on that, and I'm not even saying cos i look like shit).
When you talk to people about immortality right away they think about stuff of the past. The old school way to picture it. Vampires, life elixirs and all these crap that belong to the world of for some people still cool but pure old-fashion fantasy that aren't very helpful to help you understand the real biomedical, technological and not even science-fictional attributes of what biological (at first) immortality does really mean!
Therefore "vampires" and stories of the kind are actually counter-productive in order to study and face ageing because not so many people that I know either want to be a vampire or a zombie for some reason...
They also imagine, if they really were immortal, their own fucking boring life being endlessly unescapable.
Most people would rather pretend to be happy especially publicly, right?
Who's gonna admit:
Here we go, I just wanna die before I turn 80 and not before or later because I don't wanna have to work my ass off on this shitty job for another millennium, because my wife is already getting on my nerves after a decade but we stay together for the kids, because when I come back home every evening I'm too tired to do anything else than watching TV that has nothing else to offer than advertisements and cheap and boring reality programs once in a while, because even my friends don't amuse me anymore at times… and because living this shit forever would just be like hell on earth.
Laura Deming's speech at Ted
I wouldn't be surprised to see her multi-billionaire in 20 years
and her company one of the most life-changing of the planet
Well, I'm not Jesus or any mind fuckers of the kind promising you eternal life with no explanations whatsoever but here's the GOOD NEWS:
Future technology as biotech, nano tech and finally Artificial Intelligence or even mind-uploading won't simply give you the literally incredible power of eternal life but they will also provide the priceless ability to be whoever you want be and to do whatever you want to do whenever you want to!
You'll hopefully still have your own soul and this person that you are will be FREE and since it will also be much wiser by the exponential improvement of your intelligence there is possibly very little chances that you turn as a wicked or shitty person and get bored to death at any point!
Sure, there will also be a bunch of, still now, unpredictable problems that you'll have to face but your life will be such a blast that you would not want to go back to your previous life in a million years.
Most people would readily acknowledge how much luckier they are to live now instead than centuries ago but do they really think about why is it so?!
Sure it also have to do with politics and economics but even these stuff at the end of the day are all the little offsprings of technology, science and thoughts.
Only the power of the mind, philosophy and scientific advances could take our asses out of the awful hold that religion had on nations and people during the middle-age (just to use a single example) !
And then obviously we also live better lives for nothing much else than technological developments.
Just think about something as simple as electricity and what would happen if the whole world stopped having it and you'd get a better picture: It would basically be the end of us...
"Imagine a world without electricity"
So what does all of that has to do with immortality?
Only the fact that the "exponentiality" of technological development is the most powerful thing that has ever happened on earth, maybe the universe and even the multiverse and that if centuries ago people had to be immortal they would have had pretty good reason to get bored to death without internet, countries to travel to, other people than your neighbours to meet or even books to read!
But now things are obviously better and they will not only keep getting better but the pace of betterness (just made it up) will keep accelerating drastically until the point that not only you'd be happy to have as much time as you want for as long as you wish but you might be even a little disappointed for still not having enough time (and time won't really exist though) to do everything that you want to do even by multitasking a 100 folds and swinging between different dimensions and maybe even universes.
So, sorry about that dude but if your main concern about not wanting eternal life was because it would just turn out to be like hell on earth, apart from the fact that you won't even stick to earth on the first place, boredom is the absolute least thing you could expect from eternity and i can bet you a million years on that!
forever peace