Aging is a set of complex bio-physical-chemical processes. We have actually made a lot of progress in recent decades understanding how this happens. There is no fundamental reason we won't be able to better understand these processes and then mitigate them heavily, if not entirely.
Aubrey de Grey is one of the scientists leading these efforts and his work, along with others, is very interesting. It seems to me there is real potential here. There are many difficult hurdles, but I find it plausible we might overcome them to an extent where it is possible to significantly extend the human lifespan.
If course, if this actually happens, there will be massive social, political, and economic consequences. I'm not exactly sure how that would play out. I'm a bit of an optimist, so I imagine there would be some sort of new non-dystopic paradigm that arises.
Anyway, once they die their children will take over, as it is usual, so nothing will change if they were to just live forever.
To be fair though, my comment was way too broad. I should have clarified that I mean a constant, overbearing dread of the prospect of death is super unhealthy. Make life suck, and effectively shortens it in the experience of the scared one. (source: did that for a long time, got healthy, stopped being scared. Sample size of 1. :-D )
Reading your siblings, you're projecting your own feelings onto a completely reasonable feeling that most people have: with another hundred years of experience, what's possible?
As for projection, not so much - I've not really had any significant fear of death, aside from instinct to avoid certain demise. :-)
Instead it's more that I've only ever seen "I'm at peace with the idea of dying" and "desperately clinging to anything that can prolong my life, even if only by a little." Admittedly, that's my anecdotal experience of the people with whom I interact, and I did indeed present a false dichotomy. :-\ Again, my apologies there.
In the proper logical sense, "not wanting to die" is only technically negated as "wanting to die". Quite literally the definition of negation - introducing a "not" in front of whatever the thing is. So that's my oops.
It's a weird place though, because the negation of "at peace with the idea of dying one day" is "NOT at peace" with the same. Which implies fear. Which... I dunno, I've reached my limit now. :-)
Death is a weird concept to consider in a neutral / rational manner, eh?