Breast cancer for example is diagnosed by increasing levels of invasiveness. First a mammogram, then possibly a 3D mammogram, then an ultrasound, then a biopsy. There are possibilities for false positives all along this path and increasing levels of possible complications when performing procedures. If a false positive gets to a biopsy and you get an infection from it, you would not have ever gotten that infection if they didn't start testing you so young. False positives are very common with breast cancer screening.
Not to mention the fact that getting a biopsy can cause the cancer to spread all over the body where it might never have grown beyond its original position had it been left untouched.