The shortening of the telomeres is a protective mechanism against the development of cancer. But it only applies to non-stem-cells. In contrast, (adult) stem cells keep their telomeres intact and can divide themselves an unlimited number of times. Some of the stem cells develop into non-stem-cells when the supply of non-stem-cells becomes low.

There are many factors to aging. DNA damage, that is not repaired, accumulates over the years. And then there are also damages to the tissue on the microscopic and on the macroscopic scale that don't fully heal.