1) the first is because it may never progress to the stage where it would make the you sick,
2) the second is because you might die of something else first (sorry, I know that's morbid),
3) the third is that we don't truly understand the body's capacity to heal itself.
Using mammography as an example, the tumor it detects:
1) might not start to grow and spread until you are 110,
2) you might die of a heart attack before it grows and spreads, or
3) the tumor might shrink before it ever grew large enough to be detected during a physical. (By no means am I suggesting that all cancer resolves on its own, I'm simply saying we don't know how frequently that happens.)
The danger comes when patients undergo treatment that is harmful and unnecessary. The difficulty is that we aren't allowed to detect tumors and leave them untreated to see what happens because it isn't considered ethical (nobody wants to be the patient who needed treatment and didn't get it).
Here's a link to a study about mammographies, in particular.
And, here's a link that discusses the necessity of all sorts of tests.http://choosingwisely.org/?page_id=13
The most important thing to take away from this post is that testing is not always the best route. Don't immediately assume your medical doctor is being neglectful if he/she decides not to run a test. And, talk to your ND/MD about a serious test, making sure you understand its accuracy, validity, etc.