It is usually the case that the first knee-jerk reaction in opposition to increased human longevity is based on the mistaken belief that life-extension technologies would lead to people being ever more frail and decrepit for a very long time. This is far from the case, and it’s probably not even possible to cost-effectively engineer a society of long-lived frail people - even if that was the goal to hand. If you are frail and decrepit, then you have a high mortality rate due to the level of age-related cellular and molecular damage that is causing the failure and degeneration of your body and its organs. You won’t be around for long. No, the only way to engineer longer healthy life is to extend the period of youth and vitality, a time in which you have little age-related damage and your mortality rate is very low. Most present strategies are aimed to prolong that period of life, either by slowing the rate at which damage occurs (not so good) or finding ways to periodically repair the damage and thus rejuvenate the patient (much better).
Once people grasp that longevity science is the effort to make people younger for far longer, then the second knee-jerk objection arises. This is the belief that a very long-lived individual would become overwhelmed by boredom: they would run out of interest and novelty. This is by far the sillier objection, and there is absolutely no rational basis for it. Even a few moments of thought should convince you that there is far more to do and learn that you could achieve in a thousand life spans - and it’s a little early in the game to be objecting to enhanced longevity on the basis that you can’t think of what to do with life span number number 1001.
Considering boredom, futility, meaningless, and related matters, I noticed what appears to be an argument by induction in the article below. Mathematical induction is a tool used in formal proofs wherein if you can prove that something is generally true for n and n+1 (where n is a natural number), and then show that it is true for 1, then you can conclude it must be true for all natural numbers. If it is true for 1, then it must be true for 1+1 = 2, and true for 2+1 = 3, and so on.