Think about it.
A false positive just means you get scanned or whatever.
A false negative is far worse,,you go away all happy while the cancer grows.
Ideally a test has no false results but personally I will take a false positive any day.
You evidently are not aware of the millions of dollars of wasted health expenditures and millions of patients undergoing unnecessary suffering in the case of another cancer, prostate, because of false positives. Think about it.