zlacker

That's not entirely accurate. Telomeres shorten with age but cancers generally are triggered by mutations or defects much further in the DNA away from the telomeres.

So one hypothesis is that telomeres shrink with age which causes runaway growth (i.e. cancer) to burn up all it's telomeres early and start crunching through sequences responsible for building proteins essential to life, therefore causing some of the cancer cells to die out. Whether that hypothesis holds is a different matter but the referenced paper points towards various other mechanisms which are seemingly caused by cell age as well.