Would microwave cause meat to generate poisons that will damage our bodies, eventually we will get cancer or some weird disease?

No: This is a perennial scare story. There are even militants who claim that all cooked food is horrible. Cooking, especially char-broiling, does generates chemicals that can damage genes and contribute to the background damage from which cancer arises; microwaving probably less so.A chemical in plastic does get into microwaved food, for how, use glass / ceramic.