Many people find there to be little distance between the questions "why live longer?" and "why live at all?" It makes it hard to have conversations about the great good that might be done through the development of rejuvenation therapies without tipping over the edge into nihilistic considerations of the meaning of life. Since life has only the meaning we grant it, these tend to be circular, pointless conversations. If you wish to live, then live.
I would say that the purpose of longevity, insofar as it has one, is to make the continuation of a life worth living a choice for those who presently have no choice, tyrannized by the their own cellular biochemistry. Rejuvenation biotechnologies, like all technologies, involve expanding the human condition by adding new choices where no such choice previously existing. Indeed, the very act of choosing itself is predicated on being alive and sound to make the choice and experience the results.
"The Purposes of Longer Lives" is the theme under which the Annual Scientific Meeting of the Gerontological Society of America (GSA) will convene in November 2018. Longevity and life span have been a core focus for GSA ever since the very first issue of the Journal of Gerontology in 1946 came bannered with the slogan, "To add life to years, not just years to life." Explicit here was the idea, dating deep into recorded history, that pro-longevity efforts should seek "not merely an increase in time per se but an extension of the healthy and productive period of life."
Today, academic units concerned with gerontology have been adding the term longevity to their titles - a center for longevity, a longevity institute. This provides organizations with a measureable outcome in a way that aging by itself cannot. At the same time, credit for gains in life expectancy is due to mortality reductions at all stages of the life course.
Longevity's purpose is a teleological question about goals and ends, about the value of extended survival. Ironically, evolutionary theory about aging tells us that longer lives for organisms are pointless beyond the stage of reproduction and perhaps the rearing of offspring. If we are to find meaning in outliving this biological design, it will need to come from human and cultural aspirations for more time alive. And more time can be valuable in at least three ways: as a personal good available for any sort of individual pursuit; as a public good that benefits the larger group; and as a resource for the scientific and scholarly study of life span - research on aging thrives on more aging.