I wrote about this issue a year ago. When the prevalence of a disease in the population is less than the false positive rate of the test, when you do mass testing, then the majority of your “positive results” will be false positives.
Simple Bayesian statistics.
Vaccines and NI complicate this too – immunity means you have a fast immune response. You may have the disease, barely, momentarily, but your body is beating it down really fast. That’s how this works.
But remember, I am a brain injured idiot with no relevant experience. I make observations and ask stupid questions. Clearly, I have no idea what I am talking about here.