I want to die so my biological children can replace me: there is something essentially beautiful about it all. It speaks to life and nature, both which I have a great deal of esteem for.

That said, I don't mind life extension research but anything that threatens to end all biological life or essentially kill a human to replace it with a shadowy undead digital copy are both not worth it for it.

As another has mentioned, a lot of our fundamental values come from the opportunities and limitations of biology: fundamentally losing that eventually leads to a world without life, love or meaning. As we are holobioants, each change will have substantial downstream loss and likely not to a good end.

As far as I am concerned, immortality comes from reproduction and the vast array of behaviors around it are fundamentally beautiful and worthwhile.

The apprehension of death guides a good deal of human behavior, so the sort of entity that might arise when freed from this fate could be frightening (i.e., undergo substantial value drift in a direction that we would not approve of, like toward something akin to baby-eating). Consider how immortal beings in fiction often have hostile alien values. AI never ends well in fiction, and neither does immortality.

First, a brief summary of my personal stance on immortality:

- Escaping the effects of aging for myself does not currently rate highly on my "satisfying my core desires" metrics at the moment

- Improving my resilience to random chances of dying rates as a medium priority on said metrics, but that puts it in the midst of a decently large group of objectives

- If immortality becomes widely available, we will lose the current guarantee that "awful people will eventually die", which greatly increases the upper bounds of the awfulness they can spread

- Personal growth can achieve a lot, but there's also parts of your "self" that can be near-impossible to get rid of, and I've noticed they tend to accumulate over time. It isn't too hard to extrapolate from there and expect a future where things have changed so much that the life you want to live just isn't possible anymore, and none of the options available are acceptable.

Some final notes:

- There are other maybe-impossible-maybe-not objectives I personally care more about that can be pursued (I am not ready to speak publicly on most of them)

- I place a decent amount of prioritization pressure to objectives that support a "duty" or "role" that I take up, when relevant, and according to my estimations my stance would change if I somehow took up a role where personal freedom from aging was required to fulfill the duty

- I do not care strongly enough to oppose non-"awful" (by my own definitions) people from pursuing immortality; my priorities mostly affect my own allocations of resources

- I mentioned in several places things I'm not willing to fight over, but I am somewhat willing to explain some aspects of my trains of thought. Note, however, that I am a somewhat private person and often elect silence over even acknowledging a boundary was approached.

Because there is a very strong possibility that the "I" that achieves this immortality won't be the "I" that I have been in this biological package up to this point-the technology required may very well grossly distort (or even destroy or render irrelevant) my consciousness beyond all recognition or similarity, and I could end up as a slave or addict to the technological AI overmind in question as it subtly morphs my mind into a compromised mess.  Even if the key to I. turns out to be biological more or less, I'll almost certainly have to navigate the AI gauntlet in any event sooner or later.  I'd rather take my chances with transcending this plane altogether for a more benign and less dualistic one.

In a less dire era of history I'd be all in favor, esp. given how healthy I am right now (age 61), esp. also given how much I've honed my mind to overcome as many dualities here that I can, but all bets are off from here on out.

It could be that people regard the likelihood of being resurrected into a bad situation (e.g. as a zoo exhibit, a tortured worker em, etc.) as outweighing that of a positive outcome.

Maybe it is part of the system which protects them from the fear of death: they suppress not only thoughts about death but even their own fear of it. Similar to Freudian repression of thoughts about sex. 

I suspect a significant portion of what's going on is that there's a core kernel of truth to what they're saying - something along the lines that they're hesitant to stagnate. "not dying", to me, involves also greatly increasing my ability to change, to the point where in 500 years I'm such a different person that I'm more comparable to a descendant of myself than to my current self. I think people rightly recognize that without that level of self-mutability, extending lifespan leads to your "soul"/your informational self getting old.

the other answers have plenty of truth to them too - cope, expecting life to get worse, pessimism about the possibility, etc.

but consider: the old kind of immortality of mammalian life is the non-self-preserving kind, where you have kids, and people are very used to that and sort of intuitively know that if they live a long time they'll be messing with that deeply fundamental dynamic; I think much of what makes the mutability of selfhood of having kids good needs to be ported over to the individual self in order for serious longevity to be at all a good idea, the ability to stay mentally curious and mutable for a much much more extended period so as to continue mentally adapting to new circumstances.

I want to live forever.  I think it's vanishingly unlikely  that I will, or that anyone alive today or born in the near future will.  I think it's somewhat possible that other entities (alien or human-descended biological or cyborg, different enough that it's still effectively alien) will have a sufficiently different mechanism and conception of identity so as to be near-immortal.  

For entities of our ego-size (the unit of individual identity for humans and rate of experience-having), I think it will always be the case that replacement is far more efficient than growth and continuation. 

A lot of people just don't believe it is possible, and for good reasons. Life extension as a scientific field was around for about a century, with exactly zero results so far. And these "ASI can grant immortality" stories usually assume nanotechnology, which is most likely fundamentally impossible.

If life extension was actually available, I think attitude would be different.

For everyone who gets curious and challenges (or even evaluates on the merits) the approved right answers they learned from their culture, there's dozens more who for whatever reason don't.  "Who am I to challenge <insert authority>", "Why should I think I know better?", "How am I supposed to know what's true?" (rhetorically, not expecting an answer exists).   And a thousand other rationalizations besides. 

And then of those who try, most just find another authority they like better and end their inquiry - independent thinking is hard work, thankless work, lonely work.  Even many groups that supposedly value this adopt the language and trappings without the actual thought and inquiry.  People mostly challenge the approved right answers that the in-group has told them are safe to challenge.  Even here plenty haven't escaped this.

And obviously you already know the safe approved "right" answers from society at large on this question - it's all a trap and you're a fool for considering it.  And credit where it's due historically, they've so far been right.

Are you familiar with the concept of "religion"? You might find understanding the beliefs of so-called "death cults" helpful. There are a couple that are so popular and influential that even many who explicitly disavow them have adopted their views regarding death.