> You can just run test multiple times to eradicate this possibility

The measurements are not independent and the quality of the measurement is not improved by this.

> you can confirm it with another method.

Yes. And usually the other method is invasive and expensive and bears some risk.

And then you get results like the blood test saying "very likely cancer" and the biopsy saying "uh, probably not?" that you need to decide what to do with.

I'm confused. If this blood test gave a false positive that wasn't due to an anomaly in the blood itself, then why can't we assume that the likelihood of getting a false positive twice is lower than getting it once?

> I'm confused. If this blood test gave a false positive that wasn't due to an anomaly in the blood itself,

That's the errant part. A small amount of the false positives will be because of lab issues. The rest will be because this patient is different in some way, but not all of them are cancer. Medicine doesn't have very many perfectly specific tests.

So you have a patient who has some weird enzymes around because they're genetically different, for example, and they always pop positive on this particular test. Or has an unusual diet that causes some other non-tested-for-enzyme level to be high enough to set off this sensor. Or whatever.

In this case, the specificity is 98%, so this false positive rate is about 2%.