My contention that defeating aging should be humanity’s foremost priority rests on three statements that jointly imply it:
1) Humanity's foremost priority should be the goal that will most greatly reduce the totality of human suffering, scaled by the currently perceived probability distribution of how soon (if at all) the goal will be achieved if humanity tries really hard.
2) Aging causes most of the suffering experienced by humanity at present, and will with high probability continue to do so until it is defeated. Here I define "defeating aging" as the development, and availability to most of humanity, of medicine that mostly if not wholly eliminates the decline in physical and mental function associated with getting older.
3) Medicines that defeat aging have at least a 50% chance of being developed within the next 20 years, and given the discussion of their value that will almost certainly occur in the years preceding their arrival they will with at least 90% probability be made available to most people old enough to need them within five years following their arrival.
Regarding (1), arguments for or against utilitarianism far exceed my philosophical pay grade, so the only feature I will address is whether equal amounts of suffering of two people of different ages matter equally. Two arguable reasons exist today to give the younger person priority for life-saving medicine: it can help the younger person more, and the younger person has had less opportunity to enjoy life. But these both fail when we consider the defeat of aging: the former will simply be false, and the latter becomes negligible because both people have the expectation of far more life ahead of them than behind them.
Regarding (2), we must remember that longevity is not the goal of defeating aging but merely a side-benefit. The suffering arising from aging mostly consists of the decrepitude, dependence and disease that the elderly endure before death, the vicarious suffering of their loved ones and the indirect suffering arising from the economic burden that today's (slight) minimisation of that suffering imposes on society. Sadness arising from an elderly person's death constitutes only a minor contribution. So the important statistic, I claim, is not that most deaths are due to aging but that most sickness is.
Regarding (3), the biomedical research underlying my timeframe estimate would greatly exceed 5000 words let alone 500, so you'll just have to trust me. As for availability, the key aspect is that unlike today's (ineffective) medicines for the elderly, medicine that defeats aging will pay for itself very rapidly by eliminating the costs of treating the sick elderly, the loss of productivity of those who today must support their sick parents, and biggest of all the cost of not having the elderly contributing wealth to society. Add in the impossibility of getting elected without a commitment to universal access, and it becomes unarguable that today's restriction of access to the best medicine by ability to pay is not a valid precedent.