If you study it, it becomes pretty obvious that in most cases reproduction and death are linked. Death is fundamentally a way to optimize reproduction, to control DNA variability and number of offspring.
Also, it is obvious that death has "levels". The cells humans are made of are immortal, in the sense that human cells are capable of living and even reproducing indefinitely, if so directed by DNA. Gametes are meant to survive your death, becoming your children. Now very few cells actually do survive, but that's a constant across pretty much every immortal species. On the other hand, every cell in your body was, in a very real sense, the first bacteria, the first cell ever, billions of years ago. So it certainly is NOT the case that all human cells age, senescence, and die. Only the human as a whole ages, and it is something your cells conspire to do (or conspire not to do, in the case of ovi (~ children), or in the case of cancer cells)
At one point, during the period mammals were all still fish, evolution was still experimenting with death, and so fish have much more variation in their aging and death than mammals do. If you go back further, to reptiles, there's even less death. Most reptiles could be alive for thousands of years (even though the odds are wildly against that). Most reptiles die because of slowly advancing accumulated diseases over time (meaning over hundreds of years, a great many diseases, parasites, even physical damage, ... accumulates. No one cause is really causing their death, but combined they introduce such a strain on the organism as a whole it "dies of old age". Except it's not really of old age in the sense like humans age, it's dying of what you might call 99.9% victories against disease. Eventually the 0.1% damage per incident overpowers the metabolism)
Unfortunately this does mean that death is built into our cells and a lot of processes depend on aging and death. Therefore we are very far away from curing death: you don't just have to fix the mechanism that "ages" our cells, but you have to find alternate ways of working for everything that depends on it. Resetting the clock may be easier, but even the methods that we currently know (ie. regrowing telomeres) have a bad reputation for causing aggressive cancers, and therefore shortening life rather than prolonging it. Plus, at best if you fix aging in humans entirely, we'll be like reptiles. At that point medicine will have to radically change and every tiny trace of every minor infection will have to be treated as a life threatening condition.