There have been several reports of a significant positive correlation between paternal age and chromosome telomere length in offspring. Moreover, the telomeres in sperm cells of older men tend to be longer than in young men, and it has been concluded that telomeres lengthen in the testes during adulthood. This would be the first evidence of an increasing biological advantage with age, and therefore contradicts current models in which telomere shortening is a biomarker of aging. Instead, an alternative model of telomere erosion between human generations is discussed in which longer germ cell telomeres in old men result from their being members of a previous generation. Based on the well-known correlation between maternal age and the incidence of aneuploid pregnancies, it is hypothesized that telomere erosion predominantly operates in the female germline, leading to a carry-over effect for both sexes into the next generation. This theory fits well with experimental results that maternal age does not correlate with longer telomeres in offspring. An experimental design is presented to distinguish between the two possible scenarios leading to old fathers with long-telomered offspring - namely lifetime lengthening in the testis versus transgenerational germline erosion. Consideration of net loss of telomeric DNA between human generations is supported by recent findings of a large difference in blood telomere length between different European populations of the same age, and is likely to have profound consequences for species evolution.