What happens if cytotoxic t cells destroy cancer and viruses, then why do humans still get these diseases and tumours?

Great question!: This is one of the "holy grails" of cancer immunology research. Cytotoxic t cells are suppressed by other t cells, and some cancers and viruses create molecules that increase this suppression of cytotoxic t cells. There's also the problem of tolerance; our immune systems don't work against ourselves (usually), and cancer and viruses involve normal cells that are protected from immune attack.