I wonder why are Killer T-cells do not destroy cancer cells??

T lymphocytes or T cells, white blood cells, can guard us against most invaders and only some forms of cancer. I guess if he scientists had an answer to your question, then we wouldn't have cancer.

Also, some people just do not have strong immune systems due to diseases like MS, ALS and diabetes type 2. It is also worthy of noting that in adolescence the production of white blood cells goes over the top, and decreases as we get older, therefore, a person in their 50s or so would not be able to produce enough to ward off disease.

T cells come in 2 different types, helper cells and killer cells, they are named T cells after the thyymus, (under the breastbone), T cells are produced in the bone marrow and move later to the thymus where they mature. The killer T cells attack cells infected by viruses and bacteria. It also attacks cancer cells. It has receptors that are used to search each cell, and if infected it is killed.