We humans are, for now, the practical distinction between nature and evolution. Evolution doesn't "care" how long any individual creature lives - as long as enough members of the species live long enough to spawn the next generation. Senescence is the product of evolutionary neglect - a lack of evolutionary pressure to live longer - not part of some grand design to clear the way for future generations.
But through evolution nature produced a species that both cares about life span, and has the potential to do something about it. Senescence could not be eliminated with evolution alone. A couple more informational epochs had to come along.
But conquering senescence is only natural.
This is a sentiment that I agree with - people who argue that the fight to cure aging is "unnatural" have it all exactly backwards. Nothing is more natural than for we humans to challenge, reverse-engineer and overcome our limitations in search of a better (and longer) life.
But back to animals and aging. A somewhat better synopsis of the evolutionary explanations of aging and its oddities between species was penned by Leonid Gavrilov and Natalia Gavrilova:
The evolutionary theory of aging may be considered as part of a more general life history theory, which tries to explain how evolution designs organisms to achieve reproductive success (i.e., avoid extinction). Life history theory is based on mathematical methods of optimization models with specific biological constraints. Among the questions posed and answered by life history theory are. Why are organisms small or large? Why do they mature early or late? Why do they have few or many offspring? Why do they have a short or a long life? Why must they grow old and die? The latter two questions represent the entire scientific agenda of the evolutionary theory of aging. It could be said, therefore, that the evolutionary theory of aging is a subset of the life history theory.
Another worthy summary article for the layman can be found at Joao Pedro de Magalhaes' website.
A perhaps more striking, if overly simplistic, explanation for the existence of aging was given by Jaque Cousteau - no immortality because change is the lowest common denominator, and immortality in a species that cannot radically change itself spells extinction. It will ultimately find itself doomed by environmental changes, if not by evolutionary competition.
This doesn't preclude the possibility of an evolving clade of species with the necessary biochemistry for physical immortality; individual animals just won't have the chance to make much use of it. The Ageless Animals website provides an interesting view of outliers in the evolutionary processes that determine aging.
From where we sit, at the dawn of the biotech era, it is encouraging for our own prospects that species such as tortoises (and some whales) are capable of such extreme longevity. They aren't that different from us in the grand scheme of things, which would suggest that radical life extension via advanced biochemical and genetic manipulation - a large step beyond the present tinkering with metabolism - is a viable strategy for research in the decades ahead.