Why would it be impossible to extract dna from cooked foods?

DNA is bound together by covalent bonds between different molecules. It also contains proteins, which again are held together in their specific structures by covalent bonds.

Covalent bonds may be broken when high temperatures are applied. The temperatures that a food encounters during the cooking cause the DNA to be denatured, meaning it cannot be extracted. The same occurs with other proteins such as enzymes and antibodies.