Why does prolonged dieting or semi starvation (under 1800 calories a day) increase my chances of any cancer?

Not verified. This has not been verified in the literature. On the flip side, obesity raises your risk of multiple types of cancer. My advice would be to try to achieve and maintain an ideal body weight. Talk to your doctor about what that number range should be.
Starve Dieting. I do not know of any research that very low calorie eating increases chances of cancer. Instead, it has been shown that eating less calories, about 30%, actually increases your longevity. I also don't view 1800 cal a day as semi starvation. Most americans will maintain their weight at 1800 cal. Or gain weight, due to lack of exertion. Please notify me of your resources for your information.