Sensitivity tests are used for screening. Specificity tests are used for confirmation after positive screenings.
Sensitivity tests are used for seeing how many people truly have the disease. Specificity tests are for those who do not have the disease.
A highly sensitive test, when negative, rules OUT disease.
A highly specific test, when positive, rules IN disease. So, a test with with low sensitivity cannot rule out a disease. A test with low specificity can't rule in disease.
The doctor and patient want to screen for colon cancer and rule it out. The doctor would want a test with high sensitivity to be able to do that. He knows that testing her stool for blood will not rule out the possibility of colon CA.