Telomeres are caps on the ends of chromosomes. They get shorter each time cells divide. As the telomere caps become really short they start to interfere with cell division. This is one of the causes of aging. Telomere cap shortening is probably an evolved mechanism to reduce the risk of death from cancer. Cancers need to undergo a mutation to activate telomerase to grow longer telomere caps so that the cancer cells can divide many more times than normal cells can.
Given that shorter telomere lengths probably reduce cancer risk it is by no means guaranteed that people who inherit longer telomeres from their father will live longer on average.
If you're interested in learning more about telomeres - and the current state of knowledge regarding their place in the complex biochemical relationships between aging, cancer and cell life cycles - you should take a look and follow the links therein.
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