the counterculture "immortality is cool again actually" and its inverse are both primarily fought on 3 main fronts
Loneliness is awful; therefore eternal loneliness is worse, and it is fundamentally impossible to lose people and make new connections forever
eventually every planet you go to will be reduced to unusable inert dust and the entire universe will reach its heat death with you stuck floating there.
and lastly, and perhaps most debatable; the idea that our lives being finite is what gives them meaning.
the frankly asinine implication that an immortal lifespan would make all our accomplishments meaningless as we watched them crumble to dust in our hands. Artwork, family monuments all gone in a century.
I'm going to address that last one first because I think its frankly insulting to the concept of creation.
the argument goes (I think) that anything we make art or otherwise will lose all value by means of its language being forgotten and its pages/pillars/posts/prerequisites all being obliterated and lost to time would mean that it would be better to have never created in the first place, because there can be no "meaningful" changes in an infinite lifetime.
First off, this is wrong and anyone who makes this argument is also wrong, this point is not up for debate. the things we create and do are lost/forgotten in our own lifetime except for in the most literal sense of our cause/effect on this universe and second, to imply that action has no meaning beyond its function is to imply that things like reading and writing only exist for that short dopamine hit, that to write a poem and then burn its only copy would be a meaningless activity. I sincerely hope this argument stands for itself because if not the rest of this is going to be a tough sell
the second one is... correct-ish? I'd assume that the immortality in this hypothetical is irrevocable otherwise it kinda defeats the point and the obvious answer is just wait until a sufficiently advanced civilization frees you of your curse.
Barring that however, the universe will end but I don't think that anything that the theoretical immortal has to worry about?
If they're like kagu-moku getting sent into space wouldn't cause them to die and respawn indefinitely because they would run out oxygen in their blood in their sleep over, and over until they landed somewhere habitable.
Like a really bad cryosleep, they would wake up on some isolated star system with breathable air or that could never happen but either way no hair off their back.
Finally, the first point I made: loneliness is awful.
This one is admittedly hard. I'm going to exclude the theoretically valid "remove the pain of loneliness through brain surgery" option because if our immortal could do that they could probably lobotomize themselves and that dodges the question.
basically: yes loneliness is awful. One of the most awful things actually, and its easy to believe that after a while one would get sick of repeating that over, and over, and over however, I think its silly to imply they would give up on people "forever" I don't think thats possible. (until heat death, wherein idea 2 gets applied) but there's another option that people don't consider.
Immortality =/= perfect memory.
now depending on your perspective this might turn this from a defense of immortality into psychological horror but there is a likely chance that the immortal could live their life well into heat death without infinite suffering because they simply don't remember the million people they've met and promises they've made.
I'd argue that (in this instance) this is not only a good thing but the only way that living could function, we barely remember minor details throughout our lifetimes and ours are notable not infinite. An immortal would not only have nothing to gain from a perfect memory but it would actually almost guarantee that they could never enjoy immortal life without a literal unbreakable will.
TLDR: people give immortality too hard a time but it would be difficult as its life (which is hard but good) forever.