I don’t think the issue with screening programs is so clear-cut. There are really difficult trade-offs to be made when considering a screening program.
E.g., for breast cancer screening by mammography, the Cochrane (systematic) review puts the numbers as this:
for every 2000 women invited for screening throughout 10 years, one will avoid dying of breast cancer and 10 healthy women, who would not have been diagnosed if there had not been screening, will be treated unnecessarily. Furthermore, more than 200 women will experience important psychological distress including anxiety and uncertainty for years because of false positive findings.
Now, how do you value the one saved life against the massively lowered quality-of-life for the 10 overdiagnosed women (breast cancer treatment is no fun, I guess everyone can agree on that), not considering the stress for those with false-positive findings? I don’t know, this is really hard!
Furthermore, it is really hard to get those numbers (to base your trade-off on) more or less correct in the first place, so we’re not even quite sure on those either! Now, is it any surprising that opinions regarding mammograpy screeing are somewhat fluctuating?
[edit for correcting typos]