The mystery is that cell division isn't an issue for germline cells, like SSC, which replicate many times during your lifespan, and then keep on replicating during lifespans of all your progeny.
https://en.wikipedia.org/wiki/Spermatogonial_stem_cell
That our germline cells are immortal, yet we are not, suggests that we (our bodies) are merely a replication vessel. Humans don't live to be 150 because (according to natural selection pressures) it's easier to just make a new version of you (or several) than to waste DNA space on efforts to keep 100-year-olds alive. The genome only serves the host through child-bearing years (plus a few extra bc grandma may still be useful to the survival of her grandchildren; what happens to grandma after 90 years old the germline cares not.