Rationale behind most published works in medical imaging trying to reduce false positives
TL;DR: diseases are rare, so the absolute number of false positives is a lot more than that of false negatives.

Let's assume that our system has the same false positive and false negative rate of 1% (pretty good!), and that we're detecting the presence of new cancers this year: 439.2 / 100,000 people, or 0.5% of the population. [source]


No cancer, no detection: 99.5% x 99% = 98.5% (98.505%)
No cancer, detection: 99.5% x 1% = 1.0% (0.995%)
Cancer, detection: 0.5% x 99% = 0.5% (0.495%)
Cancer, no detection: 0.5% x 1% = 0.005%


So we can see that we have a problem: for everyone who has cancer, two people who didn't have cancer wind up with invasive surgery, chemotherapy or radiotherapy. 

For every person who fails to have a present cancer detected, two hundred people receive actively harmful treatment they didn't need and can't really afford.