Near as I can tell, the only valid point the author makes is that since mortality rates increase as cancer progresses stages and since progression through stages takes time, a 5 year mortality rate is not a great metric and it would be better to also have 10 and 15 year mortality rates to determine the degree to which early detection + treatment actually increases life expectancy.
Also, and I can’t tell if this point is made, but cancers that are more progressed are more likely to be detected without screening, so extra screening may just increase the proportion of cancers that were never going to be deadly that are detected.
That point is made.