What is right and normal and natural are not well defined. Things that reproduce well will continue to reproduce. It's not because it's the right thing to do, but because it's the thing it just so happens to do well. It's self-fulfilling. If an organism is very good at dying without leaving offspring, it won't be long before all of them are dead and there are none left in existence. By that same logic, if something is very good at staying alive and reproducing, odds are it will multiply. It's not like somehow reproduction is inherently the right thing to do, but instead it does it well because it does (and in the case of biology, through random mutations that happen to cause that). We as humans define tumors as being a disease because they often times lead to an earlier death than we are accustomed to. Our psychology and the way we think tells us it's bad to die early. But, while you may feel otherwise, there isn't a truly self evident justification for why that's the case. Rather, because we happen to feel that way, because we as humans have the notion that early death is bad, we do what we can to prevent it. Then, because we do what we can to prevent it, it happens less and less leading to more humans living longer and reproducing more. There is no origional cause other than our own notion of a desire to live long. This isnt specific to humans, as you said it's found across Animalia and other kingdoms as well. It just so happens to be for the same reason, though. Living longer is not in itself a good thing; however, the organisms that happen to think it is a good thing, whether it is or not, will take what actions they can to see to it that they live longer. Thats why even animals that arent as cognoscente as we are take action to live longer. It's not that living long and passing on genes is necessary for anything at all, but by happenstance the animals that take action and live long and reproduce will make more copies of themselves that also do the same thing over and over again.

Im sorry for repeating myself, but Im struggling to find a better way to word it. There is no inherent right or wrong, there is only what our psychology, the result of or brain chemistry, tells us is right and wrong. There is no ultimate cause for that. but, the lack of cause and justification is scary. It's not fun to feel like you do things without a purpose, so we instead substitute external ideas to imply purpose. People find religion and believe that their time in life has purpose for an afterlife. Others see having a happy life to be the justification. And some want to do good in the world for others be it volunteer work, growing family wealth or by some other means leave a legacy. But those are constructs of the human mind that distract us, or allow us to justify our actions. Without them it becomes evident that there isn't a real reason for why we do what we do.

Im just rambling at this point. I stand by what I said, but Im tired and struggling to put together anything worth reading. Sorry to waste your time!