There are various medical and physiological reasons why life forms cannot live forever in our world, but it is also important to understand the matter philosophically, because a fundamental question is whether death is important: Do we need death, or would it be better to live in a world without death? There are various perspectives and opinions regarding this question.
When I was a child, I was taught that good people go to a place where there is no killing or any other kind of death, where even formerly-carnivorous animals live in a form that does not require them to hunt, kill, or eat meat to remain alive. I do not know whether any of this is true; I do not know what Heaven is like, and I do not see much point in speculating about what Heaven is like since this is something we cannot know. What I do know is that we don't live in a world like that right now, and so practically speaking, our concern right now should be how we can live a good life in the life which we have here and now. Even so, it is important, as thinking human beings, to understand not only what is, but also what could be so that we can define goals for ourselves and understand how we could improve the status quo. This leaves us with two questions: Philosophically speaking, would it be better to live in a state where we never die, or is it better that all living things die eventually? And practically speaking, when we consider our current world, a world which is not perfect but which we could, theoretically, try to improve, what is the function of death in our present world? Is death necessary or even important?
In our current world, death is vital to new life simply because of physical space needs: A life form needs a physical space to live in, and if new life were continually created without clearing away old life, the world would eventually become filled with that biomass, because no process of expansion can continue infinitely within a finite container. If nothing else, this fact alone demonstrates how death is necessary to enable the creation of new life. This necessity could be avoided in an infinite space, but as we know, the Earth is a finite sphere. So if we were to find a way for people to biologically live forever, then we'd have a new question to answer: Would it be better to prevent new births from taking place so that the existing people could continue living, or would we need to periodically cause people to die so that new births could take place? This would put humanity in a difficult situation as it would literally require us to kill people so that new people could be born.
Theoretically, then, if we were to enable people to live forever, we could eliminate the processes of birth and death, and simply have the same people living forever. Would this be beneficial to us? There is a perspective which believes that the cycle of birth and death is critical to life. This opinion posits that just as something cannot live without being born, there can be no life without death. I have never understood this idea, because it seems illogical: I do not see why death is inherently necessary for life to exist. How people feel about this idea seems to generally be a consequence of how they feel about change versus stability: New births create a dynamic and changing world, whereas stability could be achieved by halting both births and deaths. Perhaps the more fundamental question, then, is whether it's important to grow and develop, or whether it is okay to stay the same forever. A world without birth or death would be a world in which everything could remain the same forever: Without new lives, there can be no new perspectives or ideas, because human beings are born with a particular character, and this character does not change much throughout their lives. Is it important for human beings and their societies and cultures to change from one generation to another, or is it okay that every generation lives and thinks the same way as the previous one?
There are strengths and weaknesses to both possibilities. In an unchanging society, the strength is stability: As long as conditions remain the same, that society should be relatively safe and easy to understand. The weakness in such a society is inability to adapt: If circumstances change, that society is ill-suited to adapt to changes. In a dynamic society, these advantages and disadvantages are of course reversed: A dynamic society is more readily able to adapt to change, but stability, safety, and basic understanding of life values will be lacking. In an ideal world, some kind of stability might be theoretically possible. In our non-ideal world, change is constant, which requires thinking which is able to respond appropriately to that change.
To be fair, the role of death in the process of improvement may be overrated. In the 19th century, Charles Darwin significantly impacted humanity's understanding of the facts of life with his now-famous theories about evolution, leading to the idea that the propagation of life was based on what's now commonly called the "survival of the fittest", although this phrase did not originate with Darwin, as it was coined by Herbert Spencer. In any case, this notion focuses on the idea that the weak and unfit die out, leaving the strong to survive. This, however, is only a part of evolution. This popular "kill or be killed" notion of evolution was challenged by Lynn Margulis, who near the end of her life summed up Darwinism's role in evolution by saying: "Natural selection eliminates and maybe maintains, but it doesn't create." In other words, the Darwinian concept of natural selection is not the main driver of evolution; natural selection only culls the herd, getting rid of unviable life forms, but in order for evolution to happen, new life forms need to be created, and Margulis famously asserted that this process happens through symbiosis rather than random genetic mutation and variation. Perhaps it's fitting that men pioneered a theory emphasizing the role of death in evolution, while a woman chartered a countertheory emphasizing the role of new life creation. In any case, the "out with the old, in with the new" process of evolution requires both birth and death, which means that in our world, the process of death is necessary for evolved life to appear: Life cannot flourish when it is burdened down with the task of supporting dead weight.
Ultimately, then, death is necessary in our world. Perhaps when we die, we'll go to a better place where death is no longer necessary, but again, we live in an imperfect world which needs death in order to sustain life. And indeed, not only naturally-occurring death, but also the deliberate taking of life. Most religions and secular morality systems consider murder to be immoral, but the human being is a natural killer, and this is something which cannot be separated from its physical being. Jainism is a religious whose adherents are famously so adverse to violence that they are required to walk around with brooms, sweeping the ground in front of them as they walk so as to avoid stepping on insects and thus causing death. Unfortunately for Jains, the ancient founders of their belief were not aware of the existence of microorganisms and these microorganisms' role in illness, nor of how the body's immune system is built to kill them: Every day, your body's immune system kills innumerable bacteria and other microorganisms in your body which, if left alive, would kill you instead. Jainism is based on a naive view of life in the universe which regards all life as sacred and prohibits any kind of violence or killing. From this perspective, it would be better to let people die from infectious diseases, because although this might result in the death of one person, it allows millions of microorganisms to thrive; from the quantitative perspective of life forms, then, one human life is worth sacrificing if it means that millions of other tiny life forms can be saved.
Of course, human beings are racists, and thus believe that their race is worth preserving at the expense of millions of bacterial lives. (This form of racism is generally called "humanism".) What makes human beings more worthy of life than those tiny microorganisms? Is it just that we're bigger? If size is what grants the right to live, then blue whales--the largest creatures on Earth--should be the world's main species, and all other life should exist only to serve them.
We are not the largest, fastest, or strongest creatures in the world; indeed, far from it. If we are at all worthy of life, that worth exists in our capacity for understanding and awareness: Our ability to recognize that we are, in terms of our physical bodies, programmed to do nothing but kill and consume, to understand that our lives are dependent on constant killing and subjugation, and to recognize that if we are to be alive at all, rather than eliminating these things altogether--which would be as impossible as eliminating eating and breathing--we must handle these responsibilities responsibly.
This responsibility pertains not only to microorganisms or animals who might kill us, but human beings who might do the same. It is known that criminally dangerous psychopaths exist. If one such person is a threat to public safety, they must be stopped. In a shootout situation where a clear and present danger to public safety can only be averted by shooting a criminal who would otherwise kill others (history has shown that this is not merely a hypothetical scenario), are we to risk killing the criminal to save others, or should we take the stance that life is sacred and cannot be taken, thus saving one criminal's life so that they can kill several other people?
A reality which many people do not want to acknowledge is the necessity of having killers so that other people may live. In any society, violence can erupt without warning, and so there need to be peace officers--commonly called police--who are ready to kill if necessary to protect public safety. In a larger conflict, military soldiers may be necessary. Both of these roles cannot be eliminated, not even in a peaceful society. In order for there to be happy, healthy families, there need to be deadly warriors who are prepared to kill to protect their society. You know the saying "It's a dirty job, but someone has to do it"? It's not just a cliché; it is our practical reality.
This is often interpreted as a particularly American view because the USA has historically been a major target of global terrorism, and also because it has a habit of showing off its military forces and repeating lines like "Vigilance is the price we pay for our freedom!", but the reality is that many countries--not only "Western" countries--have armed anti-terrorism forces with "shoot on sight" orders in cases of known terrorism or any other instance in which public safety is threatened. This is not something unique to America; it's a global pattern, which means it is something inherent in human beings and human society, like love and hate. The need to kill is a duty which someone needs to bear.
Of course, it can happen that the society no longer deserves its guardians. When a society is run too well and has too few problems, its people become lazy, entitled, and selfish. What happens then? Are guardians obligated to serve a people who do not deserve that service? No; in that case, the society as a whole must die so that it can be rebuilt. This is a recurring cycle throughout world history which I've mentioned before: Difficulties, problems, struggle, and suffering are necessary in a society because otherwise the people in that society become spoiled. This is, again, something which might not be necessary in an ideal world where people do not naturally become rotten, but in our real world, this is something which cannot be separated from human nature. You can imagine a perfect world, but in our real world, people need to die, and they need to suffer occasionally.
Maybe that isn't the best of all possible worlds. Maybe there are ways in which our world could be improved with different laws of science and different living things. But again, that's all theoretical, and you can imagine ideal worlds and ideal creatures if you like, but in this life which we're living right now, we cannot escape the importance of death in this world.