Since Szilard's seminal 1959 article, the role of accumulating nuclear DNA (nDNA) damage -- whether as mutations, i.e. changes to sequence, or as epimutations, i.e. adventitious but persistent alterations to methylation and other decorations of nDNA and histones -- has been widely touted as likely to contribute substantially to the aging process throughout the animal kingdom. Such damage certainly accumulates with age and is central to one of the most prevalent age-related causes of death in mammals, namely cancer. However, its role in contributing to the rates of other aspects of aging is less clear. Here I argue that, in animals prone to cancer, evolutionary pressure to postpone cancer will drive the fidelity of nDNA maintenance and repair to a level greatly exceeding that needed to prevent nDNA damage from reaching levels during a normal lifetime that are pathogenic other than via cancer or, possibly, apoptosis resistance. I term this the "protagonistic pleiotropy of chromosomal damage" (PPCD) hypothesis, because this interaction of cancer-related and -unrelated damage is the converse of the well-known "antagonistic pleiotropy" phenomenon. I then consider a selection of recent data on the rate of accumulation of nDNA damage in the context of this hypothesis, and conclude that all presently available evidence is consistent with it. If this conclusion is correct, the implications for the feasibility of greatly postponing mammalian (and eventually human) aging and age-related pathology are far-reaching.